Relevant bibliographies by topics / Vibration of triangular Plate

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Vibration of triangular Plate'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Vibration of triangular Plate"

1

Xiang, Y., K. M. Liew, S. Kitipornchai, and C. M. Wang. "Vibration of Triangular Mindlin Plates Subject to Isotropic In-Plane Stresses." Journal of Vibration and Acoustics 116, no. 1 (1994): 61–66. http://dx.doi.org/10.1115/1.2930397.

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The influence of isotropic in-plane stresses on the fundamental vibration frequencies of thick triangular plates is investigated. Some critical buckling factors are also presented in the paper. Due to the lack of results and importance of this topic, the Rayleigh-Ritz method is applied to solve the governing eigenvalue function based on the Mindlin plate theory. The fundamental frequency parameters for triangular Mindlin plates subject to uniform tensile and compressive stresses with different combinations of free, simply supported, and clamped boundary conditions are determined. The solutions are presented in the form of design charts where the fundamental frequency parameters can easily be read for particular thickness to width ratios (t/b) and in-plane stresses. Since no other vibration solution for thick triangular plate is available, the thin triangular plate solutions obtained by setting the thickness to width ratio to be very small (say t/b = 0.001), where possible, are verified with known solutions from the open literature.
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Kemparaju, H.R, and Kumar Samal Prasanta. "Detailed Numerical Study of Free Vibration Analysis of Plates." Detailed Numerical Study of Free Vibration Analysis of Plates 2, no. 2 (2019): 1–11. https://doi.org/10.5281/zenodo.3375109.

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<em>Plates are widely used in aircraft, ship building, boiler and automobile applications. It is important to study the vibration characteristics of the plates in order to avoid the resonance in their working condition. Because catastrophic failure occurs in resonance condition due violent vibrations. So to avoid these resonance condition vibration analysis of plates are very important. In this article the modal frequencies and mode shapes of the plates were analysed numerically using ANSYS. Structural steel is considered as the plate material. All edges clamped (CCCC) and all edges free (FFFF) boundary conditions were considered for the study. The effect of parameters such as aspect ratio, thickness, area and shape of the plates on natural frequency was studied. The aspect ratios of 1, 1.5, 2 and 2.5 keeping the surface are same, is considered for the study. Plates of thickness 1 mm, 1.5 mm, 2 mm and 3 mm are analysed. The effect of shape of the plate is studied by considering various shapes like square, circular, equilateral triangle and right angular triangle with same area. It is observed that the natural frequency increases with increase of aspect ratio and thickness. As the surface area increases the natural frequency decreases. The values of natural frequencies of the plates descend in the order of circular, equilateral triangular, square and right angled triangular shapes for all edges free. Whereas the values of natural frequencies of the plates ascend in the order of circular, square, equilateral triangular and right angled triangular shapes for all edges fixed conditions.</em>
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Thinh, Tran Ich, and Ngo Nhu Khoa. "A new finite element for free vibration analysis of stiffened composite plates." Vietnam Journal of Mechanics 29, no. 4 (2007): 529–38. http://dx.doi.org/10.15625/0866-7136/29/4/5603.

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A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.
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Shiau, Le-Chung, and Teng-Yuan Wu. "Free Vibration of Buckled Laminated Plates by Finite Element Method." Journal of Vibration and Acoustics 119, no. 4 (1997): 635–40. http://dx.doi.org/10.1115/1.2889774.

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Free vibration behavior of buckled composite plates are studied by using a high precision triangular plate element. This element is developed based on a simplified high order plate theory and von Ka´rma´n large deformation assumptions. The nonlinear governing equations of motion for the plates is linearized into two sets of equations by assuming small amplitude vibration of the laminates about its buckled static equilibrium profile. Results show that, in the postbuckling regime, the fundamental mode may be shifted from the first mode to the second due to squeezing effect of the in-plane force on the plate. For plate with certain boundary conditions, the natural frequency may have a sudden jump due to buckle pattern change of the plate in the postbuckling regime.
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Quintana, María Virginia, and Ricardo Oscar Grossi. "Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/252084.

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This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.
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Catania, Giuseppe, and Silvio Sorrentino. "Spectral modeling of vibrating plates with general shape and general boundary conditions." Journal of Vibration and Control 18, no. 11 (2011): 1607–23. http://dx.doi.org/10.1177/1077546311426593.

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The analysis and design of lightweight plate structures require efficient computational tools, because exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. This paper deals with vibration analysis of Kirchhoff plates of general shape with non-standard boundary conditions, adopting a Rayleigh-Ritz approach. Three different coordinate mappings are considered, using different kinds of functions: 1) trigonometric and polynomial interpolation functions for mapping the shape of the plate, 2) trigonometric and polynomial interpolation functions for mapping a constraint domain of general shape, 3) products of linearly independent eigenfunctions evaluated from a standard beam in flexural vibration for describing the transverse displacement field of the plate. Flexural free vibration analysis of different shaped plates is then performed using the same approach: skew, trapezoid and triangular plates, plates with parabolic curved edges, sectors of circular plates, circular and elliptic annular plates. Purely elastic plates are considered, but the method may also be applied to the analysis of viscoelastic plates. The results are compared with those available in the literature and using standard finite element analysis.
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Lather, Neeraj, Ankit Kumar, Parvesh Yadav, Reeta Bhardwaj, and Amit Sharma. "Vibrational frequency of triangular plate having circular thickness." Vibroengineering Procedia 52 (November 25, 2023): 67–73. http://dx.doi.org/10.21595/vp.2023.23370.

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In the current research, modes of frequency of isotropic tapered triangular plate having 1-D (one dimensional) circular thickness and 1-D (one dimensional) linear temperature profile for clamped boundary conditions are discussed. Authors implemented Rayleigh Ritz technique to solve the frequency equation of isotropic triangular plate and computed the first four modes with a distinct combination of plate parameters. Authors have performed the convergence study of modes of frequency of the isotropic triangular plate. Also, conducted comparative analysis of modes of frequency of the current study with available published papers and the results presented in tabular form. The aim of the present study is to show the impact of a one dimensional circular thickness and one dimensional linear temperature on modes of frequency of vibration of an isotropic tapered triangular plate.
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Shiau, Le-Chung, and Shih-Yao Kuo. "Free Vibration of Thermally Buckled Composite Sandwich Plates." Journal of Vibration and Acoustics 128, no. 1 (2005): 1–7. http://dx.doi.org/10.1115/1.2149388.

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A high precision triangular plate element is developed for the free vibration analysis of thermally buckled composite sandwich plates. Due to an uneven thermal expansion in the two principal material directions, the buckling mode of the plate may change from one pattern to another in the postbuckling region for certain fiber orientation and aspect ratio of the plate. Because of this buckle pattern change, the sequence of natural frequencies of the plate is also suddenly altered. By examining the buckling and free vibration modes of the plate, a clear picture of buckle pattern change and vibration mode shifting is presented. Numerical results show that if the shape of a free vibration mode is similar to the plate buckling mode then the natural frequency of that mode will drop to zero when the temperature reaches the buckling temperature.
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Crandall, Stephen H., and Wei-Qiu Zhu. "Wide band random vibration of an equilateral triangular plate." Probabilistic Engineering Mechanics 1, no. 1 (1986): 5–12. http://dx.doi.org/10.1016/0266-8920(86)90004-4.

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Papkov, Stanislav, and Jnan Ranjan Banerjee. "A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution." Mathematics 11, no. 3 (2023): 649. http://dx.doi.org/10.3390/math11030649.

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In this paper, a new method based on an accurate analytical series solution for free vibration of triangular isotropic and orthotropic plates is presented. The proposed solution is expressed in terms of undetermined arbitrary coefficients, which are exactly satisfied by the governing differential equation in free vibration. The approach used is based on an innovative extension of the superposition method through the application of a modified system of trigonometric functions. The boundary conditions for bending displacements and bending rotations on the sides of the triangular plate led to an infinite system of linear algebraic equations in terms of the undetermined coefficients. Following this development, the paper then presents an algorithm to solve the boundary value problem for isotropic and orthotropic triangular plates for any kinematic boundary conditions. Of course, the boundary conditions with zero displacements and zero rotations on all sides correspond to the case when the plate is fully clamped all around. The convergence of the proposed method is examined by numerical simulation applying stringent accuracy requirements to fulfill the prescribed boundary conditions. Some of the computed numerical results are compared with published results and finally, the paper draws significant conclusions.
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Dissertations / Theses on the topic "Vibration of triangular Plate"

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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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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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Zahn, Michael L. "Flow-induced vibration of a single flexible cylinder in a normal triangular array." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55656.

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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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McHale, Kimberley Paige Perry. "Inequalities for vibration and buckling of a clamped plate /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9842551.

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Books on the topic "Vibration of triangular Plate"

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Lucio, Maestrello, Bayliss Alvin, and Langley Research Center, eds. Coupling between plate vibration and acoustic radiation. National Aeronautics and Space Administration, Langley Research Center, 1992.

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P, Townsend Dennis, Coy John J, United States. Army Aviation Systems Command., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structure. National Aeronautics and Space Administration, 1992.

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E, Kielb Robert, ed. Joint research effort on vibrations of twisted plates: Phase 1, final results. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1985.

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H, Williams James. Modes of vibration on square fiberglass epoxy composite thick plate. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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C, Marques Elizabeth R., Lee Samson S, United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch, Massachusetts Institute of Technology, and Lewis Research Center, eds. Modes of vibration on square fiberglass epoxy composite thick plate. National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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Xiang, Y. Plate vibration with arbitrarily oriented stiffeners based on Mindlin-Engesser formulation. Department of Civil Engineering, University of Queensland, 1993.

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Y, Xiang, ed. Plate vibration with arbitrarily oriented stiffners based on Mindlin-Engesser formulation. University of Queensland, Dept. of Civil Engineering, 1993.

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L, Krantz T., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structures and the application to the reduction of gearbox vibration. National Aeronautics and Space Administration, 1995.

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L, Krantz T., and United States. National Aeronautics and Space Administration., eds. Minimization of the vibration energy of thin-plate structures and the application to the reduction of gearbox vibration. National Aeronautics and Space Administration, 1995.

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M, Morales Adolfo, and Dryden Flight Research Facility, eds. The effects of excitation waveforms and shaker moving mass on the measured modal characteristics of a 2- by 5-foot aluminum plate. National Aeronautics and Space Administration, Ames Research Center, Dryden Flight Research Facility, 1989.

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Book chapters on the topic "Vibration of triangular Plate"

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Yang, Lixiang, Yaobin Han, Xu Zhang, and Zhiwen Li. "Numerical Simulation for the Dynamic Response of Step Topography Subjected to Blasting Load." In Lecture Notes in Civil Engineering. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-2532-2_15.

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AbstractThe vibration velocity and frequency of rock mass are closely related to the instability and failure of the building. The step topography has great influence on blasting vibration wave propagation. Therefore, it is of great significance to study the dynamic response of step topography subjected to blasting load. In this paper, the FLAC2D program is used to study the dynamic response of step topography subjected to blasting load. The plane strain mode is adopted in the calculation, and the blasting load is assumed to be a triangular pulse wave which is applied to one side of the calculating mode. The amplification effect of the height of the step is first studied. The calculation result shows that the amplification factor increases first and then decreases with the increase of the step height. The maximum value of the amplification factor is consistent with the results of the field test, which indicates the feasibility of the numerical simulation.
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Pradhan, K. K., and S. Chakraverty. "Transverse Vibration of Thick Triangular Plates Based on a Proposed Shear Deformation Theory." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0287-3_1.

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Dinkler, Dieter, and Ursula Kowalsky. "Hybrid Triangular Plate Elements." In Introduction to Finite Element Methods. Springer Fachmedien Wiesbaden, 2023. http://dx.doi.org/10.1007/978-3-658-42742-9_17.

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Dinkler, Dieter, and Ursula Kowalsky. "Benchmark Concerning Triangular Plate Elements." In Introduction to Finite Element Methods. Springer Fachmedien Wiesbaden, 2023. http://dx.doi.org/10.1007/978-3-658-42742-9_20.

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Dinkler, Dieter, and Ursula Kowalsky. "Hybrid–Mixed Triangular Plate Elements." In Introduction to Finite Element Methods. Springer Fachmedien Wiesbaden, 2023. http://dx.doi.org/10.1007/978-3-658-42742-9_18.

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Preumont, A. "Piezoelectric Beam, Plate and Truss." In Vibration Control of Active Structures. Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-2033-6_4.

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Jaiman, Rajeev, Guojun Li, and Amir Chizfahm. "Theoretical Background of Flexible Plate." In Mechanics of Flow-Induced Vibration. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8578-2_12.

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Preumont, André. "Piezoelectric Beam, Plate and Truss." In Vibration Control of Active Structures. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72296-2_4.

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Sharma, Pankaj. "Vibration Analysis of FGPM Annular Plate." In Vibration Analysis of Functionally Graded Piezoelectric Actuators. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3717-8_6.

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Ma, Wenhua, and Zhenqian Li. "On Vibration Problems of Quadrilateral Plate." In Computational Mechanics ’88. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_296.

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Conference papers on the topic "Vibration of triangular Plate"

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Saadatnia, Zia, Shahryar Rahnamayan, and Ebrahim Esmailzadeh. "Vibration Analysis and Multi-Objective Optimization of Stiffened Triangular Plate." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35553.

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In this paper, nonlinear vibration of a triangular shape plate, with several stiffeners, is studied. The governing equation of transversal deflection of the plate, with considering the effects of orthotropic characteristics and external excitation, is analyzed. The ordinary differential equation for the time response of the system, through employing the Galerkin method, is obtained; and the frequency response of the plate-shape structure — using the multiple scale method — is determined. A robust genetic-based multi-objective optimization technique is employed to optimize the system’s response by finding the optimum values of the geometry and locations of the plate’s stiffeners. The influence of various parameters on the optimization results is investigated. According to the results, the optimum design of the stiffeners leads to a better performance of the vibration response.
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Inoue, Katsumi, Dennis P. Townsend, and John J. Coy. "Minimization of the Vibration Energy of Thin-Plate Structures." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0186.

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Abstract An optimization method is proposed to reduce the vibration of thin-plate structures. The method is based on a finite-element shell analysis, a modal analysis, and a structural optimization method. In the finite-element analysis, a triangular shell element with 18 degrees of freedom is used. In the optimization, the overall vibration energy of the structure is adopted as the objective function, and it is minimized at the given exciting frequency by varying the thickness of the elements. The technique of modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variables. The sensitivity is represented by the sensitivities of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. A computer code, based on the proposed method, is developed and is applied to design problems using a beam and a plate as test cases. It is confirmed that the vibration energy is reduced at the given exciting frequency. For the beam excited by a frequency slightly less than the fundamental natural frequency, the optimized shape is close to the beam of uniform strength. For the plate, the optimum shape is obtained such that the changes in thickness have the effect of adding a stiffener or a mass.
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Sabir, A. B., and G. T. Davies. "Vibration and Buckling of Square Plates Containing Central Holes." In ASME 1997 Turbo Asia Conference. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/97-aa-096.

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The finite element method is used to determine the natural frequencies of flat square plates containing centrally located circular or square holes. The plates are subjected to either inplane uniaxial, biaxial or uniformly distributed shear along the four outer edges. These edges are either simply supported or clamped. To determine the stiffness and mass matrices, non conforming rectangular and triangular displacement elements are used to model the out of plane behaviour of the plate. The inplane stress distribution within the plates, which are required in the analysis are determined by using inplane finite elements having displacement fields based on assumed strains. These satisfy the exact requirements of strain free rigid body modes of displacements. The natural frequencies of simply supported and clamped plates are initially determined when no inplane loads are applied. This showed the influence of the size of the hole on the natural circular frequency. These plates were then subjected to inplane loads and the effect of these forces on the natural frequencies are given. The results show the natural frequencies of square plates with central circular holes decrease with increasing compressive forces, and that the frequencies become zero when the compressive forces are equal to the elastic buckling loads of the plates. By repeating this process for all boundary conditions and applied loads a comprehensive set of results is obtained for the buckling and vibrational properties of square plates containing centrally located holes.
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Inoue, Katsumi, Dennis P. Townsend, and John J. Coy. "Optimum Design of a Gearbox for Low Vibration." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0064.

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Abstract A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis method, a modal analysis method, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that optimization of the top plate alone is effective in reducing total gearbox vibration.
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Sabir, A. B., and G. T. Davies. "Vibration of Square Plates Containing Eccentric Holes." In ASME 1997 Turbo Asia Conference. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/97-aa-097.

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The natural frequencies of square plates containing circular holes is investigated using the finite element method. The holes are eccentrically located, and the effect of this eccentricity on the natural frequency is examined when the plates are subjected to a variety of inplane loads. The natural frequencies are calculated by using the 12 degree of freedom non conforming rectangular and the 9 degree of freedom non conforming triangular bending elements. To determine the inplane stress distribution, strain based inplane elements are used. The displacement fields for these elements are based on assumed strain functions which satisfy the exact requirement of rigid body motion. In the present paper, the lowest natural frequencies and the corresponding modes of vibration are determined for simply supported or clamped plates containing circular holes. Initially the plate is unloaded at the middle surface, and the effect of the degree of eccentricity on the natural frequency is examined. Result are also given for plates subjected to uniform uniaxial and biaxial compression. For plates loaded by inplane uniformly distributed shear, tension and compression regions are produced. Hence for these plates, the natural frequencies are determined when the circular holes are located either in the tension or compression zones.
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Zhong, Z. W., and Chuh Mei. "Finite Element Vibration Analysis of Composite Plates With Embedded Shape Memory Alloy Fibers at Elevated Temperatures." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0630.

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Abstract The present paper investigates the vibration behavior of the thermally buckled shape memory alloy (SMA) fiber-reinforced composite plates. The stress-strain relations are developed for a thin composite lamina with embedded SMA fibers. The finite element equation of motion including shape memory effect is presented. This equation can be mathematically separated into a static equation and a dynamic equation. The thermal postbuckling deflection and vibration of the thermally buckled position for SMA fiber-reinforced composite plates are determined. Due to the effects of nonlinear material properties of SMA, the vibration characteristics of thermally buckled composite plate with embedded SMA fibers are distinctly different from the one without SMA. Thermal postbuckling, natural frequencies and vibration modes for SMA reinforced composite rectangular plates are presented. Triangular plates with simply supported and clamped boundary conditions are also studied.
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Wang, D. W., H. S. Tzou, S. M. Arnold, and H. J. Lee. "Dynamics and Active Control of Largely Deflected Active Structures Using the Finite Element Technique." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42390.

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This paper focuses on the vibration, sensing and distributed control of laminated electro/elastic nonlinear plate structures based on newly developed nonlinear shell piezoelastic finite elements. The generic governing electromechanical finite element equations for nonlinear piezoelastic shell structures are developed for the curved hexahedral and triangular piezoelectric shell elements based on the layerwise constant shear angle theory. The nonlinear system equations are linearized to enhance computational feasibility. Equations of electric potential output and feedback control force defined in a matrix from are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. Standard structural problems involving geometrical nonlinearity are tested to validate the current finite element code and verify the accuracy of the proposed hexahedral and triangular elements. Vibration control of constant-curvature electro/elastic plate structures is studied. Time-history responses of free and controlled largely deflected nonlinear electro/elastic plate systems are presented and nonlinear effects discussed.
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Monde, Masatsugu, Naoki Ono, Tomohito Nakamori, et al. "Seismic Response of Tubes Vibrating Independently in In-Plane Direction for U-Shaped Tube Bundle With Triangular Arrays in Steam Generators." In ASME 2023 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/pvp2023-105872.

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Abstract Ensuring a complete integrity of steam generators’ tubes during earthquakes is critical. In order to predict the vibration behavior of tube bundle in in-plane direction, seismic tests for U-shaped tube bundle with square arrays had been carried out. During the tests, vibrations were observed in the tube bundle at the location where the tubes and the AVBs vibrate as a whole structure. Independent vibrations for some tubes were also observed at the location where the tubes slide with the AVBs and impact with the adjacent tubes. As for the seismic design, carrying out an evaluation of the tube stress for independent vibrations was sufficient, because the maximum stress of the tubes was much larger than that of the tube bundle vibration. Since tube bundles with triangular arrays have different tube pitches, seismic excitation tests were carried out for this study, to grasp the vibration characteristics of the tubes in in-plane direction. Independent vibrations were observed for some tubes during the tests. The effects of the excitation level, the dominant frequency of excitation wave and the bending radius on independent vibration characteristics were investigated. The damping ratio of independent vibrations is mainly caused by friction force at low velocity, and by impact force with adjacent tube at high velocity. Tube stress of the independent vibration was calculated using the minimum damping ratio obtained from the tests. It was concluded that the calculation can conservatively evaluate the stress of tubes vibrating independently by comparing with the test results.
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ZHOU, R., DAVID XUE, CHUH MEI, and CHARLES GRAY. "VIBRATION OF THERMALLY BUCKLED COMPOSITE PLATES WITH INITIAL DEFLECTIONS USING TRIANGULAR ELEMENTS." In 34th Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-1321.

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Seshu, P., and V. Ramamurti. "Comparative Performance of Isotropic and Composite Bladed Disks." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0122.

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Abstract Using a 3-noded, multilayered anisotropic triangular plate and shell element combined with cyclic symmetry method, a comparison has been drawn on the steady state as well as free vibration behaviour of isotropic and composite bladed disks, taking into account all the geometric and material complexities. Results are presented for a representative model for three cases – isotropic bladed disk, isotropic disk-composite blade, and composite bladed disk.
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Reports on the topic "Vibration of triangular Plate"

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Brock, Billy C., and Armin Walter Doerry. Radar cross section of triangular trihedral reflector with extended bottom plate. Office of Scientific and Technical Information (OSTI), 2009. http://dx.doi.org/10.2172/984946.

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Cook, R. D., and D. E. Thompson. Flat Plate Vibration Analysis Experimental and Numerical Fillet Study. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada218789.

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Stevens, R. D., B. V. Chapnik, and B. Howe. L51960 Acoustical Pipe Lagging Systems Design and Performance. Pipeline Research Council International, Inc. (PRCI), 1998. http://dx.doi.org/10.55274/r0010392.

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Noise levels radiated from the exterior of a pipe wall can significantly contribute to the overall noise levels on the site of a gas plant and at neighboring properties. The noise inside the piping is generated both by the gas compressor itself, and by the flow of gas through valves, elbows and fittings. Sound inside the pipe couples to the pipe wall by exciting vibration modes, some of which are radiated from the exterior of the pipe into the air. Piping is geometrically circular, which provides it with considerable increased stiffness versus a flat plate, and thereby assists in its ability to contain low frequency sound inside the pipe. At high frequencies, where the wavelength of sound is short compared to the dimensions of the pipe, the response of the pipe approaches that of a flat plate, and considerably more sound is transmitted. Between the low and high frequency ranges lies the ring frequency, at which the wavelength of sound is equal to the circumference of the pipe; at this resonant frequency, a maximum amount of noise is transmitted out the pipe wall. For smaller pipe sizes, the ring frequency occurs above 5 kHz. For larger pipe sizes on the order of 24 inches to 36 inches, the ring frequency occurs in the range 1 kHz to 3 kHz. These frequencies fall in the most audible range of the sound spectrum. Low frequency sound is not usually of concern for pipe radiated noise, unless the source generates considerably low frequency energy. Acoustical lagging systems typically include one or more layers of porous insulation, to absorb sound and decouple vibration, and one or more layers of an impervious, heavy barrier material to contain the sound. The test configurations for this study were based on systems reported as commonly being used by PRCI member companies. Most of the member companies use fixed-in-place lagging configurations in which the various materials are applied in discrete layers to the pipe during installation. Self-contained, removable blanket systems are also in use by some member companies instead of fixed-in-place configurations, or around equipment such as valves where periodic removal of the lagging is necessary. This study provides a review of acoustic lagging systems for above ground gas piping to minimize noise.
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POWER FLOW ANALYSIS OF BRIDGE U-RIB STIFFENED PLATES BASED ON THE CONCEPT OF STRUCTURAL INTENSITY. The Hong Kong Institute of Steel Construction, 2022. http://dx.doi.org/10.18057/icass2020.p.061.

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Due to its advantages of good mechanical properties, simple appearance and strong adaptability, the steel box girder is being widely utilized in urban bridges. The noise radiated by steel box girders subjected to vehicle impacts has the characteristics of wide-spectrum, high-magnitude and control difficulty. U-rib stiffened roof, as a part of the steel box girder, directly bears the input load, which is the basis of studying the vibration of the steel box girder. Currently, the investigation on the vibro-acoustic performance of U-rib plates is very limited. With this regard, this paper introduces the concept of Structural Intensity (SI). The SI vector is calculated by the Finite Element (FE) method. The power flow is visualized by the self-programming post-processing code. The global and local vibration energy transmission characters of a U-rib stiffened plate under a harmonic nodal force are analyzed. Further, the influence of plate thickness is investigated. The optimum design is carried out based on the engineering standard dimensions. The research results indicate that increasing the thickness ratio of the U-rib to the baseplate is beneficial to reducing the vibration.
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