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1
Zhang, Lei, University of Western Sydney, of Science Technology and Environment College, and School of Engineering and Industrial Design. "Exact solution for vibration of stepped circular Mindlin plates." THESIS_CSTE_EID_Zhang_L.xml, 2002. http://handle.uws.edu.au:8081/1959.7/64.
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This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations is assembled by implementing the essential and natural boundary conditions and the segment interface conditions. Vibration solutions are presented for circular Mindlin plates of different edge support conditions and various combinations of step-wise thickness variations. These exact vibration results may serve as important benchmark values for researchers to validate their numerical methods for such circular plate problems<br>Master of Engineering (Civil)
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Zhang, Lei. "Exact solution for vibration of stepped circular Mindlin plates." Thesis, View thesis, 2002. http://handle.uws.edu.au:8081/1959.7/64.
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This thesis presents the first-known exact solutions for vibration of stepped circular Mindlin plates. The considered circular plate is of several step-wise variation in thickness in the radial direction. The Mindlin first order shear deformable plate theory is employed to derive the governing differential equations for the annular and circular segments. The exact solutions to these differential equations may be expressed in terms of the Bessel functions of the first and second kinds and the modified Bessel functions of the first and second kinds. The governing homogenous system of equations is assembled by implementing the essential and natural boundary conditions and the segment interface conditions. Vibration solutions are presented for circular Mindlin plates of different edge support conditions and various combinations of step-wise thickness variations. These exact vibration results may serve as important benchmark values for researchers to validate their numerical methods for such circular plate problems
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Huang, He. "Large-Amplitude Vibration of Imperfect Rectangular, Circular and Laminated Plate with Viscous Damping." ScholarWorks@UNO, 2014. http://scholarworks.uno.edu/td/1924.
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Large-amplitude vibration of thin plates and shells has been critical design issues for many engineering structures. The increasingly more stringent safety requirements and the discovery of new materials with amazingly superior properties have further focused the attention of research on this area. This thesis deals with the vibration problem of rectangular, circular and angle-ply composite plates. This vibration can be triggered by an initial vibration amplitude, or an initial velocity, or both. Four types of boundary conditions including simply supported and clamped combined with in-plane movable/immovable are considered.
To solve the differential equation generated from the vibration problem, Lindstedt's perturbation technique and Runge-Kutta method are applied. In previous works, this problem was solved by Lindstedt's Perturbation Technique. This technique can lead to a quick approximate solution. Yet based on mathematical assumptions, the solution will no longer be accurate for large amplitude vibration, especially when a significant amount of imperfection is considered. Thus Runge-Kutta method is introduced to solve this problem numerically. The comparison between both methods has shown the validity of the Lindstedt's Perturbation Technique is generally within half plate thickness. For a structure with a sufficiently large geometric imperfection, the vibration can be represented as a well-known backbone curve transforming from soften-spring to harden-spring. By parameter variation, the effects of imperfection, damping ratio, boundary conditions, wave numbers, young's modulus and a dozen more related properties are studied. Other interesting research results such as the dynamic failure caused by out-of-bound vibration and the change of vibration mode due to damping are also revealed.
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SALAS, JOAQUIN LEONEL SANCHEZ. "A MODEL FOR INSTABILITY AND VIBRATION OF CIRCULAR PLATES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25768@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE EXCELENCIA ACADEMICA<br>O presente trabalho mostra uma versão do método Rayleigh-Ritz com funções especializadas para a análise de placas circulares e anulares finas e espessas sujeitas a cargas fora do plano e em plano. As funções de aproximação para deslocamentos são polinómios em direção radial combinada com funções trigonométricas na direção circunferencial. Um recurso conveniente é o uso de funções nodais lineares, que permitem a fácil consideração de cargas nodais e condições de contorno (incluindo forças seguidoras), enriquecidos por polinômios de ordem superior, sem inclusão de nós adicionais. O modelo permite a variação da espessura e é aplicado em MAPLE18, possibilitando o cálculo de deslocamentos e tensões sob carregamento constante e de variação linear, as frequências de vibração, cargas de flambagem com alguns efeitos do nível de carga conservativa e não conservativa. Os exemplos mostram a eficácia desta abordagem na análise de tal estrutura e leva um novo enfoque a este problema clássico, que apresenta comparações interessantes e originais que descrevem o efeito de deformação de cisalhamento, no caso de vibrações o efeito das rotações inerciais e variação de espessura em placas circulares e anulares, incluindo deslocamentos, momentos e forças de cisalhamento, frequências de vibração, cargas de flambagem e uma análise de cargas seguidoras tangenciais não conservativas na estabilidade, utilizando o critério dinâmico é executada.<br>The present work shows a version of the Rayleigh-Ritz method with specialized functions for the analysis of thin and thick circular and annular plates subjected to out-of-plane and in-plane loads. The approximation functions for displacements are polynomials in the radial direction combined with trigonometric functions in the circumferential direction. A convenient feature is the use of linear nodal functions, which allows for easy consideration of nodal loads and boundary conditions (including follower forces), enriched by higher order polynomials without inclusion of additional nodes. The model allows for thickness variation and was implemented in MAPLE18, enabling the calculation of displacements and stresses under constant and linearly varying load, frequencies of vibration, buckling loads with a few commands and the effect of the level of conservative and non-conservative on load the stability. The examples show the effectiveness of this approach in the analysis of such structures and bring new light to this classical problem, presenting interesting and novel comparisons illustrating the effect of shear deformation, in case of vibrations of the inertial rotations analysis and thickness variation in circular and annular plates, including displacements, moments and shear forces, vibration frequencies, buckling loads and a stability analysis of non-conservative tangential follower loads, using the dynamic criterion is performed.
5
Zhang, Lei. "Exact solution for vibration of stepped circular Mindlin plates /." View thesis, 2002. http://library.uws.edu.au/adt-NUWS/public/adt-NUWS20030714.140725/index.html.
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Thesis (M. E.) (Civil) -- University of Western Sydney, 2002.<br>A thesis submitted for the degree of Master of Engineering (Civil), School of Engineering and Industrial Design, University of Western Sydney, 2002. Bibliography : p. 42-46.
6
McDaniel, James Gregory. "A new higher-order shell theory for vibration and viscoelastically-coated circular cylindrical shells." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/15825.
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Rajaona, Dominique. "Analyse harmonique de phenomenes periodiques, pseudo-periodiques superperiodiques : application a l'etude experimentale des efforts hydrodynamiques appliques sur un cylindre circulaire place dans un ecoulement stationnaire et instationnaire." Nantes, 1987. http://www.theses.fr/1987NANT2040.
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Arcas, Castillo Kevin. "Simulation numérique d'un réverbérateur à plaque." Phd thesis, Ecole Polytechnique X, 2009. http://tel.archives-ouvertes.fr/tel-00474311.
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Le réverbérateur à plaque est un dispositif électromécanique de réverbération artificielle utilisé dans les studios d'enregistrement pour traiter les signaux audio enregistrés dépourvus d'effet de salle. Ce dispositif simule la réverbération à partir des vibrations de flexion d'une plaque mince. L'objectif de cette thèse est la simulation par modèles physiques d'un réverbérateur à plaque générique permettant à l'utilisateur le choix des principaux paramètres : caractéristiques géométriques et physiques du matériau de la plaque, conditions aux limites, positions de l'excitateur et des accéléromètres, et l'influence d'une plaque poreuse à proximité. Outre la compréhension des phénomènes entrant en jeu dans de tels dispositifs, cette approche permet la simulation de réverbérateurs à plaque existants comme l'EMT-140 ou l'EMT-240, mais aussi de réverbérateurs avec d'autres jeux de paramètres réels ou fictifs. La démarche entreprise s'articule en trois points : la modélisation du dispositif, les mesures sur un réverbérateur EMT-140 et la définition des outils numériques pour la synthèse sonore dans le domaine audible. La modélisation développée relève de la dynamique et de la vibroacoustique, et porte une attention particulière sur les mécanismes d'amortissement en raison de leur grande influence dans la perception de l'effet de réverbération. La démarche expérimentale, effectuée sur un réverbérateur EMT-140, permet l'identification des paramètres d'un dispositif réel et l'identification des limites de validité de la modélisation. L'outil de simulation dans le domaine temporel repose sur la méthode des différences finies.
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Huang, Chiung-shiann. "Singularities in plate vibration problems /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487688507503742.
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Mustafa, B. A. J. "Free vibration analysis of stiffened circular shells." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/14141.
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This thesis is concerned with the free vibration analysis of stiffened circular cylindrical and conical shells. The study was carried out with a view to improving the accuracy and efficieny of various modelling techniques for the prediction of the stiffened shells natural frequencies and mode shapes. A review of the existing literature covering various aspects of the shell vibrations problem and modelling techniques has been given at the beginning of each chapter with a critical appraisal of the assumptions made and results obtained. Initially the continuum energy approach was used for the analysis. The developed method allows for discrete consideration of stiffeners having arbitrary location and properties. Energy of bending in two planes and rotary inertia have been included in the analysis. Various types of stiffened shells with shear diaphragm ends condition were analysed using this method for the prediction of their natural frequencies. The predicted results have been compared with published experimental results. The finite element technique was also used for the prediction of natural frequencies and mode shapes of stiffened shells. Axisymmetric shell of revolution element, Facet shell element, semi-100f element and various types of beam elements, which are available within the PAFEC 75 suite of programs, were used for these studies. An efficient modelling technique has been introduced for ring stiffened cylindrical and conical shells by the use of the shell of revolution element. For improved accuracy of the predicted frequencies and a more economical model, shell symmetry was utilized for the free vibration analysis of unstiffened and stiffened shells. Half, quarter and one eighth models were studied by developing the appropriate boundary conditions and are discussed here. The free vibration characteristics of orthogonally stiffened cylindrical shells and an orthogonally stiffened cylindrical panel have been studied. An eight noded stiffened super shell element was developed for this study. This element was used for modelling various other types of stiffened shells and the predicted natural frequencies have been compared with known published experimental and theoretical results. Experimental verification of theoretical predictions of natural frequencies and mode shapes of an orthogonally stiffened cylindrical panel was carried out and is reported here.
11
Rosen, Oren. "Sturm-Liouville extensions : applications in plate vibration /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2006. http://uclibs.org/PID/11984.
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Bercin, A. N. "High frequency vibration analysis of plate structures." Thesis, Cranfield University, 1993. http://dspace.lib.cranfield.ac.uk/handle/1826/10030.
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Noise and vibration are important design issues for many types of vehicles such as ships, cars, and aeroplanes. Structure borne sound, which may be of relatively high frequency, usually emanates from an engine or some other type of localised source and propagates through the vehicle. Excessive vibration levels, and thus structural damage, may occur while structural acoustic interactions may lead to unacceptable interior noise. In the analysis of energy transmission between plate structures, it is common practice to consider only bending modes (or waves) of the structure. However if the concern is with high frequency vibration analysis, then due allowance may need to be made for the presence of inplane shear and longitudinal modes. Due to the infeasibility of the industry standard technique, the Finite Element Method, at high frequencies, almost all of the studies that have investigated the importance of in-plane energy transmission have used Statistical Energy Analysis (SEA). In this study an existing dynamic stiffness method is extended to include in-plane effects, and used as a benchmark against which SEA is assessed. Additionally the Wave Intensity Analysis (WIA) technique, which is an improved form of SEA, is extended to in-plane vibrations, and used to identify some of the reasons for the poor performance of SEA in certain applications. All three methods are applied to a wide range of plate structures within the frequency range of 600 Hz to 20 kHz. While the response levels as predicted by the WIA are generally quite close to exact results, it has been found that although all of the requirements which are usually postulated for the successful application of SEA are fulfilled, SEA severely underpredicts the energy transmission in large structures because of the diffuse wave field assumption. It is also shown that the exclusion of in-plane modes may lead to sizeable errors in energy predictions unless the structure is very simple.
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Hanna, Nagy F. "Thick plate theories, with applications to vibration /." The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683049374286.
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Robu, Bogdan. "Active vibration control of a fluid/plate system." Phd thesis, Toulouse 3, 2010. http://thesesups.ups-tlse.fr/1103/.
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Cette thèse s’intéresse au problème du contrôle actif des vibrations structurelles d’une aile d’avion induites par le ballottement du carburant dans les réservoirs qu’elle contient. L'étude proposée ici est concentrée sur l'analyse d'un dispositif expérimental composé d'une longue plaque rectangulaire en aluminium équipée d'actionneurs et de capteurs piézoélectriques et d'un réservoir cylindrique. La difficulté principale réside dans le couplage complexe entre les modes de vibration de l’aile et les modes de ballottement du liquide. Un modèle de ce dispositif à l’aide d’équations aux dérivées partielles est tout d’abord construit. Ce modèle de dimension infinie couple une équation des plaques avec l'équation de Bernoulli pour le mouvement du fluide dans le réservoir. En analysant la contribution énergétique des modes, une approximation en dimension finie, de type espace d'état est alors construite. Après une méthode de recalage fréquentiel du modèle, un contrôle est réalisé en utilisant dans un premier temps une méthode par placement de pôle et dans un deuxième temps, la théorie de la commande robuste H-infini. La dimension du modèle et les performances demandées imposent le calcul d’un contrôleur H-infini d'ordre réduit, conçu en utilisant la librairie HIFOO 2. 0 et testé sur le dispositif expérimental pour différents niveaux de remplissage. Finalement, le problème de la correction simultanée avec un correcteur HIFOO d'ordre réduit est aussi analysé<br>We consider the problem of the active reduction of structural vibrations of a plane wing induced by the sloshing of large masses of fuel inside partly full tank. This study focuses on an experimental device composed of an aluminum rectangular plate equipped with piezoelectric actuators/sensors at the clamped end and with a cylindrical tip-tank, more or less filled with liquid, at the opposite free end. The control is performed through piezoelectric actuators and the main difficulty comes from the complex coupling between the flexible modes of the wing and the sloshing modes of the fuel. First, a partial derivative equation model is computed by coupling a plate equation with a Bernoulli equation for the fluid motion. After analyzing the energetic contribution of each mode, a state space approximation is established. After a model matching procedure, a control is computed by using the pole placement method and the H-infinity theory. Due to the large scale of the synthesis model and to the simultaneous performance requirements, a reduced-order H-infinity controller is computed using the HIFOO 2. 0 package and tested on the experimental device for different filling levels. Finally, the problem of simultaneous control with a reduced order HIFOO controller is tackled. Experimental results of this non-convex optimization problem are given and commented
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Mohammadpanah, Foroutaghe Ahmad. "Idling and cutting vibration characteristics of guided circular saws." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/40416.
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In this thesis the vibration characteristics of guided circular saws are studied, both analytically and experimentally. Significant insights into the complex dynamic behavior of guided circular saws are presented first by numerical investigation of rotating disks and then by conducting idling and cutting experimental tests of splined saws with different guide configurations.
For the numerical investigations, the governing linear equation of transverse vibration of a rotating disk is used. As a primary interest, the variation of disk natural frequencies with rotation speed and the disk response to applied external force are calculated. Also, the steady state response of the disk at different speeds is calculated. The effects of elastic lateral constraints are investigated in this section.
A comprehensive experimental investigation of idling tests of splined saws with different guide configurations is presented. The frequencies and amplitudes of the blade vibrations are documented and the mean deflections of the disks are plotted. The dynamic characteristics of a rotating blade when subjected to the stationary lateral constant force are discussed.
Extensive cutting tests are conducted and the effect of different guide configurations on cutting accuracy is presented. Cutting tests are conducted at different speeds, below and above the lowest critical speed for different guide configurations. The cutting results are compared to determine the guide configuration which results in the best cutting accuracy.
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Prasad, Suryanarayana A. N. "Two-port electroacoustic model of a piezoelectric composite circular plate." [Gainesville, Fla.] : University of Florida, 2002. http://purl.fcla.edu/fcla/etd/UFE0000594.
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Jane, Kuo Chang. "Buckling, postbuckling deformation and vibration of a delaminated plate." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/19975.
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Md, Salleh Salihatun. "Active intelligent control of vibration of flexible plate structures." Thesis, University of Sheffield, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.538085.
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Vergeer, Pieter. "Vibration isolation of dimple plate heat exchangers / Pieter Vergeer." Thesis, North-West University, 2012. http://hdl.handle.net/10394/8455.
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Dimple plate heat exchangers are a new type of welded compact plate
heat exchangers. The dimple plates increase the turbulence of the fluid
flowing over the plate, increasing the efficiency of the heat exchanger
without increasing pressure drop over the heat exchanger. The compact
design of the heat exchanger makes it possible to install the heat
exchanger at the top of condenser columns, reducing the footprint area
of the column by replacing standard shell and tube condensers at the
foot of the column.
After the implementation of these condensers in 2008, Sasol
experienced failures of 12 column-top dimple plate condensers in unit
300. In these cases damage was observed at the weld between the
plates and the bottom header. One possible reason for the damage was
vibration caused by the flow over the dimple plates.
The characteristics of flow-induced vibrations in dimple plate heat
exchangers were studied in the scientific literature. It was, however,
found that although the effect of dimples on channel walls had been wellresearched,
the fluid-elastic vibration of the bluff body containing the
dimples had not been sufficiently studied. A simple aerodynamic model
was constructed to determine the characteristics of the combination of
vibration caused by the bluff body (plate) and the flow over the dimples
on the plate. The experiment showed the generation of two flow-induced
vibration amplitudes.
The structure of the heat exchanger was modelled by using mass,
stiffness and damping elements. With certain assumptions the model
was reduced to a two degrees of freedom system that simulated the
most prominent vibration direction. This model was used to simulate the
effect of design changes to the response of the structure to a range of
forcing frequencies. An experimental model of the column-top condensers was constructed
and the response due to different vibration frequencies was measured.
The measured results were compared with the theoretically predicted
values for cases with the current design and the cases where the
vibration-control concept was implemented. This validated the theoretical
model and the mathematical simulation as a tool to design vibrationcontrol
systems for real heat exchangers.
With the replacement of the very stiff mounts that are used in current
designs with soft rubber mounts, the dynamic forces on the internal
plates was reduced by up to 97.8% for certain forcing frequencies. The
deflection of the internal plates is a main cause of stress in the plates
and, more importantly, the weld fillets connecting the bottom of the plates
to a common header. This repeated stress can easily cause fatigue
failure in the welds. By therefore reducing the amplitude of vibration of
the heat exchangers, the onset of fatigue failure will be substantially
delayed, increasing the reliable lifetime of the column-top condenser.
This concept is not only limited to dimple plate heat exchangers. The
oscillating stress in any internal component can, therefore, be reduced
by isolating the whole system with soft rubber mounts of a determined
stiffness and layout.<br>Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012
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Wen-YuLiang and 梁文宇. "Axisymmetric Free Vibration of Transversely Isotropic Circular Plate." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/95425663704912517736.
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碩士<br>國立成功大學<br>土木工程學系碩博士班<br>98<br>On the basis of the state space approach, the axisymmetric free vibration of transversely isotropic circular plate is analyzed. The state equation of axisymmetric free vibration of transversely isotropic circular plate is established from three-dimensional basic equations of elasticity in the cylindrical coordinates. By using separation of variables, the components of displacements and stresses are expressed as a superposition of two sets of particular solutions of the state equation with enough coefficients to satisfy arbitrary boundary conditions and determine the frequencies for the free vibration of plate. The results for the transversely isotropic and the isotropic plates are presented, and the latter are compared with those based on the linear shear-deformation Mindlin plate theory.
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Huang, Chien-Hang, and 黃健航. "Vibration Analysis of Circular Plate with Radial Crack." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/13520947757655095453.
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碩士<br>中原大學<br>機械工程研究所<br>94<br>ABSTRACT
The analysis of vibration for the simply supported circular plate with an edge crack is presented. The governing equation and displacement function of classical theory is considered in vibration analysis. Using the frequency values of Yuan, Young and Dickinson solved by Rayleigh-Ritz method to fitting a fundamental natural frequency polynomial and curve. The vibration analysis includes free vibration and force vibration. The equations of vibration are reduced to an ordinary differential equation by assuming mode shapes and Galerkin’s procedure. Then compare the error percentage of fundamental natural frequency for different authorities. By using of the Runge-Kutta method, the amplitude for different crack ratios and excited frequency with free vibration and force vibration are determined from the Mathieu equation. The results and diagrams are provided in this study dividedly. One can find that during the vibration of the cracked circular plate, the natural frequency decreases with the crack depth. The unsteady relation of vibration with frequency and amplitude for cracked circular plate is the major accomplishment in this study.
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Ding-KeWang and 王丁科. "Vibration Analysis of Piezoelectric Circular Plate under Uniform Load." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/bu3equ.
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碩士<br>國立成功大學<br>工程科學系<br>105<br>This study presents the analysis of a circular piezoelectric plate subjected to a uniform load. The circular host plate is aluminum and the bottom surface bonded with a piezoelectric plate. The governing equations and the corresponding boundary conditions of the entire system are obtained by performing Hamilton’s principle. The finite element technique is set for analyzing the behavior of the entire plate. The shape functions of one element are obtained by solving the equations of static equilibrium. The effects of thickness and area of the piezoelectric layer on the displacement of the plate and the electric charge accumulation on the bottom piezoelectric layer are to be investigated.
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Ke, Jyh-Liang, and 柯至良. "Nonlinear Random Vibration Analysis of a Nonuniform Orthotropic Circular Plate." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/42570353782822331176.
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碩士<br>國立中興大學<br>應用數學研究所<br>81<br>In this paper, the dynamic response of geometrically nonlinear
circular plates under random excitation has been investigated.
This kind of problem has wide ranges of application in civil
engineering, mechanical engineering and aerospace
engineering. Von Karman plate theory in conjunction with
Galerkin technique has been adopted to obtain the dynamic
response of nonlinear circular plates in terms of the
deflection component. The above procedure gave a nonlinear
ordinary differential equation involving the deflection
component, which can be solved by stochastic equivalent
linearization technique. Finally, the statistical dynamic
response of the circular plates such as deflection, strain and
stress has been calculated and checked by Monte Carlo
simulation.
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Hsu, Jui-Long, and 徐瑞隆. "Development on Solution Method for the Vibration of Non-Uniform Circular Plate." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/77536786259544020066.
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碩士<br>國立成功大學<br>機械工程學系碩博士班<br>93<br>The governing characteristic differential equation for the axisymmetric vibrations of a non-uniform circular plate is a regular singular fourth-order ordinary differential equation with variable coefficients. If the variable radial thickness of the circular plate varies in arbitrary polynomial form, then the four fundamental solutions can be derived and expressed in exact closed forms. One also shows that the third derivatives of the two fundamental solutions are singular at the center of the circular plate. The natural frequency equation of the system is expressed in terms of the fundamental solutions. The exact general solution of the static deflection of a non-uniform plate with general elastically restrained boundary conditions is developed in closed integral form. This study is concerned with application of normalized fundamental solutions’ relation and Green’s function to the force vibration of circular plate with variable thickness. The Green’s function for the circular plate with homogeneous boundary conditions and various loading is presented and expressed in terms of four normalized fundamental solutions of the system. Finally, the numerical results are compared with those in the existing literatures.
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Lee, Yen, and 李炎. "Vibration analysis of stepped circular plates." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/12747102073905970029.
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Chen, Ge Tzung, and 陳格宗. "AXISYMMETRIC VIBRATION ANALYSIS OF CIRCULAR PLATES." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/58107989920149997733.
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Jang, Jyh-Jye, and 張智傑. "Vibrations of a Composite Rotating Circular Plate." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/55300280963144131195.
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碩士<br>國立成功大學<br>機械工程學系<br>86<br>AbstractIn this text, the natural frequencies and membrane
stresses of the symmetrically laminated polar orthotropic
annular plates are investigated.The formulation is initiated
from the fundamental equations of theory of elasticity. With
membrane stresses due to rotation considered and with
assumptions of plates theory introduced, the governing
differential equations of the system are derived. Base on these
equations, responses of free vibration are analyzed. In the
analysis of free vibration: the transverse deflection of an
annular plate is expanded in angular direction by Fourier series
so that the two-dimensional equations (in space) can be reduced
to the one-dimensional ones. By using finite element method, the
preceding equations are solved for natural frequencies. The
results reveal that plates with higher stiffness ratio or
Poisson's ratio have higher natural frequencies and certain
laminations are capable of producing a higher fundamental
frequency than either of the constituent materials alone can
attain.
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蔡增祥. "Vibration Analysis of a Taper-cross Section Circular Plate using Finite Element Method." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/85132426431551417775.
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碩士<br>國立屏東科技大學<br>機械工程系<br>91<br>This project apply Finite Element Analysis method to study the natural frequencies and modal shape of taper-cross section circular plate under the influence of different parameters such as ratios of thickness to outer radius, ratio of inner to outer radius, taper constant and angular velocity of rotation etc, and find optimum parameters association by taiguchi Method. The results of Finite Element Method analysis show the natural frequencies will increase according as ratios of thickness to outer radius, ratio of inner to outer radius and angular velocity of rotation increase, but will decrease according as taper constant increase. For a bigger effect of structure resonance in low frequencies, the modal shape has limited effects under the range of parameters setting in this paper. We can get the level of influence for different parameters on natural frequencies by taiguchi Method, and find optimum parameters association rapidly, comparing with tradition experimental modal analysis. The combination of Finite Element Method and taiguchi method greatly decrease the time and expense. The results and method of this study could be referred to as the design of non- uniform section circular plate.
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HUANG, JUN-REN, and 黃俊仁. "Vibration and stability of thick circular plates." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/84764434967575270263.
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Shukla, Sanjay Kumar. "Experimental Study of Flow Past a Circular Cylinder with a Flexible Splitter Plate." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/2961.
Full textAbstract:
A circular cylinder is a geometrically simple bluff body that occurs in various practical applications. As with any bluff body, it exhibits large drag forces and a strong fluctuating lift force, both related to the strong shedding of vortices from the body, which is commonly referred to as the Karman Street. Rigid splitter plates in the wake of the cylinder are known to suppress shedding from the body, and thereby result in reduced drag and fluctuating lift forces, the latter being important to reduce flow-induced vibrations of the body. In the present work, the flow past a cylinder with a downstream flexible splitter plate/flap is studied, the length (L) and flexural rigidity (EI) of the flap being the main parameters besides the flow speed (U). Two flaps length to cylinder diameter ratios (L/D), namely, a short (L/D = 2) and a long (L/D = 5) flaps have been studied, the shorter one being smaller than the recirculation zone, while the larger is longer than the recirculation zone. In both these cases, the flexural rigidity (EI) and the flow speed are systematically varied. In all cases, the flaps motion are directly visualized, the lift and drag forces are measured with a force balance, and the wake velocity field is measured using PIV.
In both the long and short flaps cases, the flexural rigidity (EI) of the flexible flap has been varied over a large range of values, and it has been found that the results for flaps tip motion and forces collapse well when plotted with a non-dimensional bending stiffness (K∗), which is defined as K∗ = EI/(1/2ρU2L3). This collapse occurs across flexible flaps with different values of EI, as long as Re > 5000. The collapse is not found to be good for Re < 5000. This difference appears to be related to the large reduction in fluctuating lift for a bare cylinder in the Re range between approximately 1600 and 5000 discussed by Norberg[41].
In the long flap case, the existence of two types of periodic modes is found within the range of K∗ values from 5 × 10−6 to 1 × 10−1 studied. The first one corresponds to a local peak in amplitude at K∗ ≈ 1.5 × 10−3 that is referred to as mode I, and the second that occurs at low values of K∗ (K∗ < 3 × 10−5) that is referred to as mode II. The fluctuating lift is found to be minimum for the mode I oscillation. The mean drag is also found to reach a broad minimum that starts at K∗ corresponding to mode I and continues to be at the same low level of approximately 65% of the bare cylinder drag for all higher K∗ values, representing an approximately 35% decrease in mean drag of the cylinder. The wake measurements also show significant changes with K∗. The formation length (lf /D) obtained from the closure point of the mean separation bubble is found to continuously increase with K∗, reaching values of approximately 2.6 at mode I and thereafter only small increases are seen as K∗ is increased to large values corresponding to the rigid splitter plate case, consistent with the observed variations in the mean drag. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode I case compared to the bare cylinder case, and more importantly, these values are even lower than the rigid splitter plate case. This is consistent with the shedding of weaker vortices and with the minimum in fluctuating lift found in the mode I case. The results for this flap length show that the mode I flap oscillation, corresponding to K∗ ≈ 1.5 × 10−3, may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices. In particular, the wake fluctuations corresponding to this mode are found to be significantly lower than the rigid splitter plate case.
In the short flap case (L/D = 2), it is found that there exists a richer set of flapping modes compared to the long flap, with these modes being dependent on K∗. At low K∗ values, the flap exhibits large amplitude symmetric flap motion that is referred to as mode A, while clearly asymmetric flaps motion are seen at higher K∗ values corresponding to modes B and C. Mode B corresponds to asymmetric large amplitude flapping motion, while mode C is also asymmetric with the flap clearly deflected off to one side, but
having small oscillation amplitudes. At even higher K∗ values, corresponding to mode D, symmetric flaps motion are again seen with the amplitudes being smaller than in mode A. Apart from the flap tip amplitude, the non-dimensional frequency of flap tip motion also changes as the flap changes modes. In this case, there is a minimum in the fluctuating lift corresponding to mode B and C oscillation. The mean drag is found to reach a minimum again corresponding to mode C, which corresponds to an approximately 35% decrease in mean drag of the cylinder. In this case, there is a large increase in fluctuating lift (approximately 150% of the bare cylinder case) at higher values of K∗ that appears to correspond to a “resonant” condition between the structural natural frequency of the flexible splitter plate/flap and the wake shedding frequency of the bare cylinder. The wake measurements show that the formation length (lf /D) is the largest for mode C (deflected flap state), which is consistent with the observed minimum in mean drag observed for this mode. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode C case compared to the bare cylinder case, with the values for the Reynolds shear stress being lower than the rigid splitter plate case. This is again consistent with the minimum in fluctuating lift found in the mode C case. The results for this flap length show that the mode C flap oscillation, corresponding to K∗ ≈ 5 × 10−2 that correspond to a deflected flap state with very small oscillation may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices.
The results from the present study show that the flexible flap/splitter plate down-stream of the cylinder exhibits a variety of mode shapes depending on the effective bending rigidity of the flap K∗ for both the long and short flaps cases. The forces and the wake are also found to be strongly dependent on this parameter K∗ with the wake fluctuations, lift fluctuations and the drag being very effectively suppressed at an intermediate value of K∗ that is found to be dependent on the plate/flap length.
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Shukla, Sanjay Kumar. "Experimental Study of Flow Past a Circular Cylinder with a Flexible Splitter Plate." Thesis, 2017. http://etd.iisc.ernet.in/handle/2005/2961.
Full textAbstract:
A circular cylinder is a geometrically simple bluff body that occurs in various practical applications. As with any bluff body, it exhibits large drag forces and a strong fluctuating lift force, both related to the strong shedding of vortices from the body, which is commonly referred to as the Karman Street. Rigid splitter plates in the wake of the cylinder are known to suppress shedding from the body, and thereby result in reduced drag and fluctuating lift forces, the latter being important to reduce flow-induced vibrations of the body. In the present work, the flow past a cylinder with a downstream flexible splitter plate/flap is studied, the length (L) and flexural rigidity (EI) of the flap being the main parameters besides the flow speed (U). Two flaps length to cylinder diameter ratios (L/D), namely, a short (L/D = 2) and a long (L/D = 5) flaps have been studied, the shorter one being smaller than the recirculation zone, while the larger is longer than the recirculation zone. In both these cases, the flexural rigidity (EI) and the flow speed are systematically varied. In all cases, the flaps motion are directly visualized, the lift and drag forces are measured with a force balance, and the wake velocity field is measured using PIV.
In both the long and short flaps cases, the flexural rigidity (EI) of the flexible flap has been varied over a large range of values, and it has been found that the results for flaps tip motion and forces collapse well when plotted with a non-dimensional bending stiffness (K∗), which is defined as K∗ = EI/(1/2ρU2L3). This collapse occurs across flexible flaps with different values of EI, as long as Re > 5000. The collapse is not found to be good for Re < 5000. This difference appears to be related to the large reduction in fluctuating lift for a bare cylinder in the Re range between approximately 1600 and 5000 discussed by Norberg[41].
In the long flap case, the existence of two types of periodic modes is found within the range of K∗ values from 5 × 10−6 to 1 × 10−1 studied. The first one corresponds to a local peak in amplitude at K∗ ≈ 1.5 × 10−3 that is referred to as mode I, and the second that occurs at low values of K∗ (K∗ < 3 × 10−5) that is referred to as mode II. The fluctuating lift is found to be minimum for the mode I oscillation. The mean drag is also found to reach a broad minimum that starts at K∗ corresponding to mode I and continues to be at the same low level of approximately 65% of the bare cylinder drag for all higher K∗ values, representing an approximately 35% decrease in mean drag of the cylinder. The wake measurements also show significant changes with K∗. The formation length (lf /D) obtained from the closure point of the mean separation bubble is found to continuously increase with K∗, reaching values of approximately 2.6 at mode I and thereafter only small increases are seen as K∗ is increased to large values corresponding to the rigid splitter plate case, consistent with the observed variations in the mean drag. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode I case compared to the bare cylinder case, and more importantly, these values are even lower than the rigid splitter plate case. This is consistent with the shedding of weaker vortices and with the minimum in fluctuating lift found in the mode I case. The results for this flap length show that the mode I flap oscillation, corresponding to K∗ ≈ 1.5 × 10−3, may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices. In particular, the wake fluctuations corresponding to this mode are found to be significantly lower than the rigid splitter plate case.
In the short flap case (L/D = 2), it is found that there exists a richer set of flapping modes compared to the long flap, with these modes being dependent on K∗. At low K∗ values, the flap exhibits large amplitude symmetric flap motion that is referred to as mode A, while clearly asymmetric flaps motion are seen at higher K∗ values corresponding to modes B and C. Mode B corresponds to asymmetric large amplitude flapping motion, while mode C is also asymmetric with the flap clearly deflected off to one side, but
having small oscillation amplitudes. At even higher K∗ values, corresponding to mode D, symmetric flaps motion are again seen with the amplitudes being smaller than in mode A. Apart from the flap tip amplitude, the non-dimensional frequency of flap tip motion also changes as the flap changes modes. In this case, there is a minimum in the fluctuating lift corresponding to mode B and C oscillation. The mean drag is found to reach a minimum again corresponding to mode C, which corresponds to an approximately 35% decrease in mean drag of the cylinder. In this case, there is a large increase in fluctuating lift (approximately 150% of the bare cylinder case) at higher values of K∗ that appears to correspond to a “resonant” condition between the structural natural frequency of the flexible splitter plate/flap and the wake shedding frequency of the bare cylinder. The wake measurements show that the formation length (lf /D) is the largest for mode C (deflected flap state), which is consistent with the observed minimum in mean drag observed for this mode. The stream wise and cross-stream turbulent intensities and the Reynolds shear stress are all found to be strikingly lower in the mode C case compared to the bare cylinder case, with the values for the Reynolds shear stress being lower than the rigid splitter plate case. This is again consistent with the minimum in fluctuating lift found in the mode C case. The results for this flap length show that the mode C flap oscillation, corresponding to K∗ ≈ 5 × 10−2 that correspond to a deflected flap state with very small oscillation may be useful to reduce lift, drag, velocity fluctuations in the wake and the strength of the shed vortices.
The results from the present study show that the flexible flap/splitter plate down-stream of the cylinder exhibits a variety of mode shapes depending on the effective bending rigidity of the flap K∗ for both the long and short flaps cases. The forces and the wake are also found to be strongly dependent on this parameter K∗ with the wake fluctuations, lift fluctuations and the drag being very effectively suppressed at an intermediate value of K∗ that is found to be dependent on the plate/flap length.
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Ya-Kue, Shiu, and 許亞奎. "Free vibration analysis of circular plates with multiple circular holes using BIEMs." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/81242114008784579859.
Full textAbstract:
碩士<br>中華技術學院<br>機電光工程研究所碩士班<br>95<br>In this thesis, a semi-analytical approach for eigenproblem of circular plate with multiple circular holes is presented. Natural frequencies and natural modes are determined by the null-field integral formulation in conjunction with degenerate kernels, tensor rotation and Fourier series. All the kernels in the direct formulation will be expanded into degenerate (separate) form. By uniformly collocating points on the boundary and taking finite terms of Fourier series, a linear algebraic system can be constructed. The direct searching approach will be adopted to determine the natural frequency through singular value decomposition (SVD). After determining the unknown Fourier coefficients, the corresponding mode shape will be obtained by using the boundary integral equations for domain points. The results of the annular plate, as a special case, will be compared with the analytical solution to verify the validity of the present method. For the cases of circular plates with an eccentric hole or multiple circular holes, the present method will be also compared with the existing approximate analytical method or finite element method (ABAQUS). Besides, the effect of eccentricity of the hole on the natural frequencies and modes will be also considered. Good accuracy, high rate of convergence and computational efficiency will be the main features of the present method due to the semi-analytical procedure.
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Dai, Ching-Liang, and 戴慶良. "Analysis and Control of A Vibrating Circular Plate." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/97870109951992337729.
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林辰彥. "Vibration induced by harmonic loadings applied at circular rigid plate on layered half-space medium." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/76236813452565858717.
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Yang, Shun-Chi, and 楊順吉. "Identification of Arbitrary Boundary In-plane Force for Circular Plates Using Vibration Measurements." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/17724517375174998487.
Full textAbstract:
碩士<br>大同大學<br>機械工程研究所<br>91<br>This research is concentrated on the isotropy circular plates of the fixed outer diameter after being exercised with arbitrary in-plane forces; and then, we adopt the partial differential characteristic equations of Galerkin method to deduce the responding frequency approximations, together with the best solution to figure out the sensitivity of the tension against responding frequency. The arbitrary in-plane forces can be unfolded to the type of Fourier Series and also converted into non-dimension in-plane stress equation to be calculated into the governing equation of circular plates with the resultant theoretically responding frequencies. When comparing the responding frequency values from both theory deduction and experiments, we also modify the Fourier series parameters hypothesized by theory to result in the congruence between experimental and theoretical responding frequencies.
Within this research, we will apply the eigen-sensitivity methods to the searching of the sensitivity parameters for the forces against responding frequencies so that it can shorten the duration to search the parameters of Fourier series. Also, when it exists in the congruence between theory and experiment, we come to understand the magnitude and distributing shapes of the in-plane forces. We can adopt the Modal Assurance Criterion (MAC) to identify the vibration types of various modes from both experiment and theory by mode shapes.
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Li-YingTung and 董立瑩. "Vibration of circular plates by 3-D elasticity theory." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/49034498120683778525.
Full textAbstract:
碩士<br>國立成功大學<br>土木工程學系碩博士班<br>101<br>Free vibration of transversely isotropic circular plates is analyzed on the basis of theory of elasticity without a priori plate assumptions. The governing equations for vibration of transversely isotropic circular plates are derived from the three-dimensional equations of elasticity in the cylindrical coordinates. By means of separation of variables, two sets of solutions are obtained, which enable us to satisfy various edge boundary conditions of the problems and determine the natural frequencies of the circular plates. Numerical results are evaluated and compared with those obtained according to the classical plate theory.
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Zhou, Zhi-Hao, and 卓志豪. "Transverse Vibration Investigation for the Piezoceramic Composite Circular Plates." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/64624596419334750486.
Full textAbstract:
碩士<br>清雲科技大學<br>機械工程研究所<br>98<br>This thesis investigates the transverse vibration characteristics of piezoceramic composite plates under different boundary conditions by applying the electroelasticity and Kirchhoff plate theory. By comparing the characteristic equations of resonant frequencies between isotropic and piezoceramic-metal composite disks, the named equivalent Poisson’s ratio and bending stiffness are derived, and then the transverse vibration characteristic equation can be expressed as single formulation. The numerical calculations obtained by finite element method (FEM) and a optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), are also employed to validate the theoretical analysis. It is shown that the theoretical predictions, including the resonant frequencies and mode shapes, agree rather well with numerical results and experimental measurement. Through means of the concept of equivalent constants, the resonant frequencies and mode shapes of annuli under different boundary conditions are also obtained. According to the theoretical calculation, the variations in resonant frequencies versus the various layer-thickness ratios for annuli with different boundary conditions are investigated in the thesis.
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chen, Chien-hao, and 陳建豪. "Vibration Analysis of Circular Plates Subjected to Preshearing Loading." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/86190956167492799321.
Full textAbstract:
碩士<br>國立中山大學<br>機械與機電工程學系研究所<br>99<br>The present study proposes a simple and relatively complete displacement field, which, with the finite element formulation, can be employed in the analyses of the free vibration of circular and annular plates, the vibration with preloading in the radial direction, which is studied quite often, and the vibration with preloading under twisting, which has not yet appeared in the literature.
The present results of the free vibration and the vibration under compressive stresses for circular and annular plates with different boundary conditions and various aspect ratios will be compared with those by ANSYS and other research. From the comparisons, we know that the present method does not need a fine mesh to get accurate natural frequencies of the plates.
As to the vibration for the bar or tube with pretorsional loading, coupled vibration modes in the r-z plane and θ direction, it can be revealed by the present method, and the appearance of these vibration modes may be due to the coupling terms from the proposed displacement field. Also, these vibration modes have not been shown before.
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Lin, Shu Yu, and 林淑瑜. "Experimental Investigation of Vibration of Composite Plates with Circular Cutouts." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/46109635879423122737.
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Tseng, Ching-Shiung, and 曾慶祥. "Free Vibration of Polar Orthotropic Laminated Circular and Annular Plates." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/89971676215639244826.
Full textAbstract:
碩士<br>國立中興大學<br>應用數學研究所<br>83<br>According to first-order shear deformation plate theory and
applying 8-node isoparametric element，a”displacement finite-
element model”is established to discuss the free vibration
behaviors of polar-orthotropic laminated circular and annular
plates．The effects of different boundary conditions、lamina
stacking sequences and hole-radius ratios on the frequencies
and mode shapes of composite laminated plates are analyzed．
Numerical results show that frequencies and mode shapes are
related to these effects and the thickness of plates．
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LIN, QING-YU, and 林慶瑜. "Vibration analysis of thin circular plates with partially restrained edge." Thesis, 1990. http://ndltd.ncl.edu.tw/handle/56164485814962391188.
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Ju, Kuo-Peng, and 朱國鵬. "Nonlinear Axisymmetric Vibration of Circular Plates with Random Geometric Imperfections." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/25754393119050646226.
Full textAbstract:
碩士<br>國立成功大學<br>航空太空工程學系<br>81<br>Effects of random initial geometric imperfection on non- linear
dynamic response of axisymmetric circular plates sub- jected to
external random pressure are investigated in this thesis using
the Monte Carlo method. Governing equations are those of Von
Karman's moderately large deflection equations of motion for
thin plates, modified to account for an initial geometric
imperfection. Initial imperfection and external pr- ssure are
assumed to be Gaussian random prosses and are simu- lated
numerically. Lindsted-Poincare's perturbation technique is
employed to solve the nonlinear differential equation der- ived
for vibration analysis of imperfect circular plates. The method
of equivalent linearization is applied to obtain an approximate
solution for nonlinear random vibration of the imperfect
circular plates which are axisymmetric wtih postb- uckled
condition. A time domain Monte Carlo method is used for
nonlinear response analysis of imperfect plates for various
boundary conditions. It is shown that the effects of random
geometric imperfections on the vibrational behavior of the
plates can be described quantitatively in terms of the frequ-
ency reliability function and probabilities of both sanp thr-
ough vibration and hard-spring behavior.
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Shih, Chih-Hung, and 施志鴻. "Vibration and Sound Radiation of Flexibly Supported Circular Laminated Composite Plates." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/ekd79e.
Full textAbstract:
碩士<br>國立交通大學<br>機械工程系所<br>92<br>Vibration characteristics and sound radiation of flexibly supported circular laminated composite plates are studied in this thesis. Using both theoretical and experimental means, we investigate how layer angles and laminated composite structure affect the sound radiation of the flexibly supported circular plates. The effects of continuous and discontinuous flexible suspensions on the SPL of the same circular plates were studied.
The flexible suspension using PU foam was formed through a process of heating and pressing and the stiffness of the suspension was measured from experiments. In analysis, elastic springs were used to simulate the flexible suspensions.
The dynamic behaviors of the circular laminated composite plates and circular sandwich plates were studied based on the Classical Laminated Plate Theory or the First Order Shear Deformation Theory, and the Ritz method was used with a power series as the displacement function to yield natural frequencies and natural models of the circular plates. In the part of SPL calculation, we established the models of the circular composite plates using ANSYS for harmonic response analysis. And then we used the calculated amplitude and phase of each element in the circular plate to construct the SPL spectrum. Furthermore, the effects of different variables, such as lamination angle, plate thickness, stiffness of springs on the trend of the SPL curves were also studied.
In the experimental study, we made circular composite laminated plates and sandwich plates. And then we proved that the solutions of theoretical analysis were consistent with the experimental results of SPL and natural frequencies. The results provided in this thesis may be of value for designing circular radiating panels having efficient radiation capability.
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Wang, Horng-Jou, and 王宏洲. "Vibration and Dynamic Stability of Circular Plates with Constrained Damping Layer." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/88407711161039084421.
Full textAbstract:
博士<br>國立成功大學<br>機械工程學系碩博士班<br>91<br>Vibration, damping and dynamic stability of sandwich circular plates with constrained damping layer are investigated. The governing equations of sandwich circular plate system are derived by a discrete layer annular finite element method. The transverse shear effects are included in the finite element, and it is convenient to handle the thick or thin plate problem. The material properties of isotropic, linear and incompressible viscoelastic materials in damping layer are described by complex representations. The free vibration and dynamic stability of stationary and rotational sandwich circular plates are the focus of this thesis. In the mathematical modeling, initial stress distribution induced by rotational and external load effects are obtained from the solutions of static problems and are taken into account in the strain energy expression to calculate the geometry stiffness matrices. The governing equations with complex coefficients are derived, and natural frequencies, modal loss factors and boundaries between dynamic stability region and instability region can be solved.
The effects of many design parameters, such as stiffness and thickness of the damping and constraining layers, treatment sizes and rotational speeds, are discussed. Numerical results are shown that the thicker damping layer or the larger treatment size is not always provided better damping properties of plate systems. The modal loss factors of systems are decreased with increasing of rotational speeds. Moreover, the effects of the constrained damping layer tend to stabilize circular plate systems.
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Chun-Ying, Hwang, and 黃春穎. "AXISYMMETRIC FINITE ELEMENT VIBRATION ANALYSIS OF TAPER-CROSS SECTION CIRCULAR PLATES." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/92096646730749843327.
Full textAbstract:
碩士<br>國立中山大學<br>機械工程學系<br>87<br>Free axisymmetric vibration of annular plates of taper-cross section have been analysis by the classical theory of plates . It only research the natural frequency of transverse vibration and interpret not enough detailedly about the vibration motion of thickness . Due to three-dimensional-elasticity modified finite element , discussion the natural frequencies and the modal shapes of taper-cross section plates by using eigenvalue technique . Without adding any assumption and predigest , it is more conveniently and exactly to simulate the axisymmetric vibration of three dimension annular plates than those classical plate-theory in practically . Natural frequencies of annular plates with different taper constants , ratios of inner-to-outer radius , geometry and boundary conditions are derived by present approach and are compared with those by plate-theory approach .
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Mohapatra, Arpita. "Free Vibration Study of Annular Laminated Composite Circular Plates with Holes." Thesis, 2015. http://ethesis.nitrkl.ac.in/7774/1/2015_Free_Vibration_Mohapatra.pdf.
Full textAbstract:
A composite laminate is layers of fibres of composite materials which are assembled to provide desired engineering properties. These have a wide range of application, especially in weight sensitive structures like aircraft, spacecraft. Laminated plates used in these structures are subjected to dynamic loads. These plates with numerous circular cut outs are either used to lessen the mass of the whole structure or to expand the inspection. The presence of cut outs in the plates changes the stress distribution of the plates and makes the analysis complex. When an external system vibrates has exactly the same natural frequency as the internal system, resonance follows producing considerable deflections. Specific plans can minimise these unnecessary failures. Hence the analysis of the modal characteristics of these plates is significant. First an isotropic circular plate’s behaviour is studied and then a circular orthotropic plate has been considered for this study. The material properties have been fixed. The natural frequencies have been computed for different boundary condition, hole-radius ratio, and thickness to radius ratio, and fibre orientation, asymmetric and symmetric holes. The effects of these variables on the nature of vibration have been analysed and discussed. ANSYS 13.0 is used for the computation of natural frequencies.
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Ji, Ming, and 紀明. "Theoretical Analyses of Free Vibrations Based on Higher Order Plate Theories for a Thick Circular Piezoelectric Plate." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/89896085080898748147.
Full textAbstract:
碩士<br>國立臺灣大學<br>機械工程學研究所<br>103<br>This paper presents the free vibration analyses of transversely isotropic circular plate and piezoelectric circular plate based on Reddy plate theory and Leissa plate theory. Governing equations and boundary conditions of transversely isotropic circular plate are derived from Hamilton’s principle.To validate the plate theories, the resonant frequencies and mode shapes of in-plane and out-of-plane vibrations are compared with those obtained from finite element analysis.Then the higher order plate theories are employed to obtain results of free vibrations for piezoelectric circular plates.The results of theoretical analyses are in good agreements with the results of numerical analyses. Finally,the two complete theories,Reddy plate theory and Leissa plate theory,which are useful and accurate are developed for establishing free vibration frequencies and mode shapes.
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Ying-Te, Lee, and 李英德. "Thee dimensional vibration analysis of circular and annular plates under axisymmetric loads." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/54304855557907785939.
Full textAbstract:
博士<br>國立中山大學<br>機械工程學系<br>88<br>In the dissertation, a modified axisymmetric finite element is proposed to analyze the 3-D vibration frequencies of circular and annular plates under
1. different combinations of radius-to-thickness ratio, inner-to-outer radius, and boundary condition.
2. plus axisymmetric in-plane loading, or
3. plus rotation of the plates.
For most of the cases above, frequencies of both axisymmetric and unaxisymmetric modes are derived. Buckling load is also obtained for the preloading cases. As to the rotating cases, Coriolis effect is considered for some cases. Both the preloading and rotating cases, frequencies are calculated with and without initial deformation considered.
Due to the 3-D nature of the present approach, it is able to reveal all the possible vibrating modes and to satisfy exactly all types of displacement boundary conditions, with or without imposing different axisymmetric preloading, including centrifugal force of rotation. Initial deformation due to initial loading is also considered in the present study and is shown to have tremendous effect on the vibration frequency for some cases. Also, typical problems are analyzed and results of the present approach are compared with those by other methods.
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Shukla, Sanjay Kumar. "Flow Over A Circular Cylinder With A Flexible Splitter Plate." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/732.
Full textAbstract:
Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate can deform due to the fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted like in the rigid splitter plate case. In particular, we study two kinds of flexible splitter plates. In the first case, the splitter plate is rigid but is flexibly mounted (hinged) to the cylinder, while in the second case, the entire splitter plate is flexible. We are interested in both the dynamics of the splitter plate, if they do vibrate at all, and in the wake dynamics downstream of the flexible splitter plates. The main parameters in the problem are the splitter plate length (L) to cylinder diameter (D) ratio, the relative mass of the plate, the Reynolds number, and the stiffness and internal damping associated with the flexible plate. In our study, we investigate this problem in the limit where the stiffness and internal damping of the plate are negligible and hence are not parameters of interest.
For the hinged-rigid splitter plate case, experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force in this case, and has been seen previously for elastically-mounted cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45D,where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter (L/D) ratio is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L/D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The non-dimensional oscillation frequencies (fD/U ) on the other hand are found to continuously vary with L/D from fD/U ≈ 0.2at L/D =1 to fD/U ≈ 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D ≥ 5.0. It appears that the vortex shedding is nearly inhibited for L/D ≥ 4.0 in the present case. This is also supported by measurements of the wake vorticity field from Particle-Image Velocimetry (PIV). The phase-averaged PIV vorticity fields show that the strength of the shed vortices decreases rapidly as the splitter plate length increases. For longer splitter plates, L/D ≥ 4.0, the plate oscillations are no longer periodic, and hence it appears that the wake vortices are not synchronized with the splitter plate motions.
For the entirely-flexible splitter plate case, the splitter plate deformations appear to be in the form of a travelling wave. In this case, the tip amplitudes are significantly larger of the order of 1.1D, and the non-dimensional oscillation frequency (fD/U )is close to 0.2, approximately the same as the Strouhal number for the bare cylinder. In sharp contrast to the hinged-rigid splitter plate case, the non-dimensional amplitude and frequency appear to be nearly independent of the normalized splitter plate length (L/D)even up to L/D =7.0. PIV measurements of the wake vorticity field indicates that there appears to be a nearly continuous sheet of vorticity on both sides of the flexible splitter plate, and the vortex sheet sheds and forms distinct vortices only at the trailing edge of the plate. The strength of these shed vortices appears to be close to that of the bare cylinder at similar Re. The results appear to suggest that in this entirely-flexible case, the vortices form at the same frequency and are of the same strength as in the bare cylinder case, but their formation is just pushed further downstream. This would suggest that in this case, the base suction and drag could be lower than the bare cylinder. Further, the formation of vortices further downstream of the body could imply that this type of flexible splitter plate could be useful to suppress vortex-induced vibrations (VIV).
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Shukla, Sanjay Kumar. "Flow Over A Circular Cylinder With A Flexible Splitter Plate." Thesis, 2008. http://hdl.handle.net/2005/732.
Full textAbstract:
Previous work on rigid splitter plates in the wake of a bluff body has shown that the primary vortex shedding can be suppressed for sufficiently long splitter plates. In the present work, we study the problem of a flexible splitter plate in the wake of a circular cylinder. In this case, the splitter plate can deform due to the fluid forces acting on it, and hence the communication between the two sides of the wake is not totally disrupted like in the rigid splitter plate case. In particular, we study two kinds of flexible splitter plates. In the first case, the splitter plate is rigid but is flexibly mounted (hinged) to the cylinder, while in the second case, the entire splitter plate is flexible. We are interested in both the dynamics of the splitter plate, if they do vibrate at all, and in the wake dynamics downstream of the flexible splitter plates. The main parameters in the problem are the splitter plate length (L) to cylinder diameter (D) ratio, the relative mass of the plate, the Reynolds number, and the stiffness and internal damping associated with the flexible plate. In our study, we investigate this problem in the limit where the stiffness and internal damping of the plate are negligible and hence are not parameters of interest.
For the hinged-rigid splitter plate case, experiments show that the splitter plate oscillations increase with Reynolds numbers at low values of Re, and are found to reach a saturation amplitude level at higher Re. This type of saturation amplitude level that appears to continue indefinitely with Re, appears to be related to the fact that there is no structural restoring force in this case, and has been seen previously for elastically-mounted cylinders with no restoring force. In the present case, the saturation tip amplitude level can be up to 0.45D,where D is the cylinder diameter. For this hinged-rigid splitter plate case, it is found that the splitter plate length to cylinder diameter (L/D) ratio is crucial in determining the character and magnitude of the oscillations. For small splitter plate lengths (L/D ≤ 3.0), the oscillations appear to be nearly periodic with tip amplitudes of about 0.45D nearly independent of L/D. The non-dimensional oscillation frequencies (fD/U ) on the other hand are found to continuously vary with L/D from fD/U ≈ 0.2at L/D =1 to fD/U ≈ 0.1 at L/D = 3. As the splitter plate length is further increased beyond L/D ≥ 4.0, the character of the splitter plate oscillations suddenly changes. The oscillations become aperiodic with much smaller amplitudes. In this long splitter plate regime, the spectra of the oscillations become broadband, and are reminiscent of the change in character of the wake oscillations seen in the earlier fixed-rigid splitter plate case for L/D ≥ 5.0. It appears that the vortex shedding is nearly inhibited for L/D ≥ 4.0 in the present case. This is also supported by measurements of the wake vorticity field from Particle-Image Velocimetry (PIV). The phase-averaged PIV vorticity fields show that the strength of the shed vortices decreases rapidly as the splitter plate length increases. For longer splitter plates, L/D ≥ 4.0, the plate oscillations are no longer periodic, and hence it appears that the wake vortices are not synchronized with the splitter plate motions.
For the entirely-flexible splitter plate case, the splitter plate deformations appear to be in the form of a travelling wave. In this case, the tip amplitudes are significantly larger of the order of 1.1D, and the non-dimensional oscillation frequency (fD/U )is close to 0.2, approximately the same as the Strouhal number for the bare cylinder. In sharp contrast to the hinged-rigid splitter plate case, the non-dimensional amplitude and frequency appear to be nearly independent of the normalized splitter plate length (L/D)even up to L/D =7.0. PIV measurements of the wake vorticity field indicates that there appears to be a nearly continuous sheet of vorticity on both sides of the flexible splitter plate, and the vortex sheet sheds and forms distinct vortices only at the trailing edge of the plate. The strength of these shed vortices appears to be close to that of the bare cylinder at similar Re. The results appear to suggest that in this entirely-flexible case, the vortices form at the same frequency and are of the same strength as in the bare cylinder case, but their formation is just pushed further downstream. This would suggest that in this case, the base suction and drag could be lower than the bare cylinder. Further, the formation of vortices further downstream of the body could imply that this type of flexible splitter plate could be useful to suppress vortex-induced vibrations (VIV).