Relevant bibliographies by topics / Natural frequencies of free vibration

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Academic literature on the topic 'Natural frequencies of free vibration'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Natural frequencies of free vibration"

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Günay, M. Gökhan. "Free Transverse Vibration of Nickel Coated Carbon Nanotubes." International Journal of Structural Stability and Dynamics 21, no. 06 (2021): 2150085. http://dx.doi.org/10.1142/s0219455421500851.

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Transverse vibration of nickel coated carbon nanotubes is investigated by using molecular dynamics simulations. The simulations are carried out for armchair and zig-zag carbon nanotubes with various lengths. Uncoated and nickel coated carbon nanotubes having same lengths are analyzed and their vibrational behaviors are compared. Free transverse vibrations of nickel coated carbon nanotubes are modelled by using a two-phase local–nonlocal Euler–Bernoulli beam model and solved by finite element method. Nonlocal parameter of the beam model is calibrated based on molecular dynamics simulation results. It is seen that for the same length diameter ratio, the nickel coated carbon nanotubes have similar vibrational characteristics with the uncoated carbon nanotubes but their natural frequencies are smaller than the uncoated ones. Also, it is shown that by using proper nonlocal parameters for each radius length ratio, the two-phase local–nonlocal Euler–Bernoulli beam model can successfully predict the natural frequencies of both short and long nanotubes. Besides natural frequencies and mode shapes, the clustering of nickel atoms depend on simulation temperature which is discussed during oscillation of nickel coated carbon nanotubes.
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Smirnov, Andrey L., and Grigoriy P. Vasiliev. "Natural frequencies of an inhomogeneous square thin plate." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 2 (2021): 212–19. http://dx.doi.org/10.21638/spbu01.2021.202.

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Plates, which geometric and physical parameters slightly differ from constant and depend only on the radial coordinate, are analyzed. For free vibration frequencies of a plate, which thickness and/or Young’s modulus depend on the radial coordinate asymptotic formulas are obtained by means of the perturbation method. As examples, free vibrations of a square plate with parameters linearly or parabolically depend on the radial coordinate, are examined. The double frequencies of square plates with similar edge support of all edges are of special interest, since any variation of the thickness or stiffness causes some loss of symmetry one may expect the split of double frequencies. The asymptotic formulas permit to determine, which of two equal unperturbed frequencies corresponding to wave numbers n and m increases faster with the small parameter. For a wide range of small parameter values, the asymptotic results for the lower vibration frequencies well agree with the results of finite element analysis with COMSOL Multiphysics 5.4.
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Fabian Sarquis de Campos, Cássio, Daniele Araújo Altran, and Gustavo Figueiredo Formagio. "ANÁLISE COMPARATIVA DOS MODOS E FREQUENCIAS NATURAIS DE VIBRAÇÃO DE VIGAS ENGASTADA LIVRE E BI-ENGASTADA SUJEITAS À OSCILAÇÕES LIVRES." COLLOQUIUM EXACTARUM 10, no. 4 (2018): 18–27. http://dx.doi.org/10.5747/ce.2018.v10.n4.e252.

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The objective of this work was the theoretical and computational modeling of free-form and bi-set beams, objectively showing their ways of vibrations and their natural frequencies. The study of the dynamics of rigid or flexible structures, under the action of external forces, such as regular marine waves, winds, external mechanical vibrations of any order, is of extreme importance for the prevention of possible structural problems, for example, displacements, partial or total ruptures of these structures. All the study was carried out Recebido em: 10/08/2018Revisado em: 28/08/2018Aprovado em: 20/09/2018 19Colloquium Exactarum, v. 10, n.4,Out-Dez. 2018, p.18–27. DOI: 10.5747/ce.2018.v10.n4.e252using the methods of Computational Analysis of the Natural Vibration Modes and Frequencies of a Free Beam of Forms for Free Frequencies and Computational Calculation of Lies and Natural Vibration Frequencies of a Beam Without Free Sets of Free Oscillations and the Computational Computation of Lies and Natural Frequencies of Vibration of a Bi Beam established by the Method ofAssumed Modalities. The computational resources used to do the theoretical remodeling of the beams and their functions were Matlab®and Maple®. Employees to implement three-dimensional vibration modes and development of new studies with different bundles and physical properties. This comparative work of the beams provided the mathematical and dynamic knowledge of modeling of the structures, being they, modeling skills through programming.
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Mohamed Salleh, Muhammad, and Izzuddin Zaman. "Finite Element Modelling of Fixed-Fixed End Plate Attached with Passive Vibration Absorber." Applied Mechanics and Materials 773-774 (July 2015): 194–98. http://dx.doi.org/10.4028/www.scientific.net/amm.773-774.194.

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Every vibration structure has a certain resonance which tends to oscillate with larger amplitude at certain frequencies. These frequencies are known as resonance frequencies or natural frequencies of the structure. At these resonance frequencies, even a small periodic force can result the structure to vibrate excessively. Thus, in this study, the free and forced vibrations of fixed-fixed ends plate were simulated using a commercial Finite Element Analysis software, such as ANSYS to investigate the natural frequencies, mode shape and the response of the plate. Later, the vibration absorber is attached to the plate in order to decrease the vibration amplitude produced by a shaker. The preliminary result shows that the plate vibration reduced significantly with attached a single vibration absorber.
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Singh, Deepak Kumar, Priyaranjan Pal, and S. K. Duggal. "Free Vibration Analysis of Lock Gate Structure." Journal of Mechanics 36, no. 4 (2020): 507–20. http://dx.doi.org/10.1017/jmech.2020.10.

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ABSTRACTThe effect of fluid on the natural frequencies of a vertical rectangular lock gate is investigated. The fluid is assumed to be inviscid and incompressible having an irrotational flow field. The far boundary of fluid domain is truncated near the lock gate structure by solving the Laplace equation using Fourier half range cosine series expansion. The formulation of lock gate structure is governed using Mindlin’s plate theory. The coupled interaction between the fluid domain and the lock gate structure is established using finite element method (FEM) and a computer code is written using FORTRAN. Convergence study and validation of the formulation are carried out to minimise the computational error. The natural frequencies of lock gate coupled with and without fluid are determined for undisturbed and linearised free surface conditions. By varying extent of fluid domain, the effect on the natural frequencies of lock gate is evaluated. The results of natural frequencies obtained may be useful to the designer when the reservoir lock gate structure is exposed to the natural disasters.
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San, Bingbing, Yunlong Ma, Zhi Xiao, Dongming Feng, and Liwei Yin. "Stochastic Natural Vibration Analyses of Free-Form Shells." Applied Sciences 9, no. 15 (2019): 3168. http://dx.doi.org/10.3390/app9153168.

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This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.
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Yang, Xiao-Dong, Zhen Li, Wei Zhang, Tian-Zhi Yang, and CW Lim. "On the gyroscopic and centrifugal effects in the free vibration of rotating beams." Journal of Vibration and Control 25, no. 1 (2018): 219–27. http://dx.doi.org/10.1177/1077546318774246.

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This paper addresses the gyroscopic and centrifugal effects on vibrations of rotating Bernoulli–Euler beams. The gyroscopically coupled system is established as a complex eigenvalue problem. It is concluded that there exist three types of velocity-dependent terms that contribute to the natural frequencies with different effects. In particular, the contribution of gyroscopic terms and static and dynamic centrifugal terms to the natural frequencies are discussed for free vibrations of rotating beams with constant angular velocity. On the other hand, the vibrations in different directions coupled through the gyroscopic terms are investigated. Some numerical examples for the elliptic vibration modes in the rotating plane are presented and the results reveal the actual vibration contour of the rotating beams.
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Peng, Li, and Ying Wang. "Differential Quadrature Method for Vibration Analysis of Prestressed Beams." E3S Web of Conferences 237 (2021): 03029. http://dx.doi.org/10.1051/e3sconf/202123703029.

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This paper investigates natural frequencies of free transverse vibrations of prestressed beams, and the governing equations and natural frequencies of the free vibration in related literatures are discussed and corrected. The differential quadrature methods (DQ) are applied directly to the corrected governing equations to get the the values of natural frequency numerically. Under the simple supported boundary conditions, the natural frequencies of model beam are numerically studied, and the physical parameters of the beam are analyzed respectively. The numerical results show that the natural frequency values increase with the growth of concrete strength and eccentricity of prestressed steels. But with the increase of the span length of beam and values of original prestressing force, the natural frequency values decrease.
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Tsay, Alex Y., Jin-Hui Ouyang, C. P. Roger Ku, I. Y. Shen, and David Kuo. "Free Vibration Analysis of PZT Glide Heads." Journal of Tribology 121, no. 4 (1999): 984–88. http://dx.doi.org/10.1115/1.2834166.

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This paper studies natural frequencies and mode shapes of a glide head with a piezoelectric transducer (PZT) through calibrated experiments and a finite element analysis. In the experiments, the PZT transducer served as an actuator exciting the glide head from 100 kHz to 1.3 MHz, and a laser Doppler vibrometer (LDV) measured displacement of the glide head at the inner or outer rail. The natural frequencies were measured through PZT impedance and frequency response functions from PZT to LDV. In the finite element analysis, the glide head was meshed by brick elements. The finite element results show that there are two types of vibration modes: slider modes and PZT modes. Only the slider modes are important to glide head applications. Moreover, natural frequencies predicted from the finite element analysis agree well with the experimental results within 5% of error. Finally, the finite element analysis identifies four critical slider dimensions whose tolerance will significantly vary the natural frequencies: PZT bonding length, wing thickness, slider thickness, and air bearing recess depth.
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Nguyen, Duong Huong, Long Viet Ho, Thanh Bui-Tien, Guido De Roeck, and Magd Abdel Wahab. "Damage Evaluation of Free-Free Beam Based on Vibration Testing." Applied Mechanics 1, no. 2 (2020): 142–52. http://dx.doi.org/10.3390/applmech1020010.

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Damage can be detected by vibration responses of a structure. Damage changes the modal properties such as natural frequencies, mode shapes, and damping ratios. Natural frequency is one of the most frequently used damage indicators. In this paper, the natural frequency is used to monitor damage in a free-free beam. The modal properties of the intact free-free beam are identified based on a setup of 15 accelerometers. A finite element model is used to model the free-free beam. Three models are considered: beam (1D), shell (2D), and solid (3D). The numerical models are updated based on the first five bending natural frequencies. The free-free beam is damaged by a rectangle cut. The experiment is re-setup and the model properties of the damaged beam are re-identified. The cuttings are modeled in the numerical simulations. The first five numerical bending natural frequencies of the damaged beam are compared with the experimental ones. The results showed that the 1D beam element model has the highest errors, while the 2D and 3D models have approximately the same results. Therefore, the 2D representation can be used to model the damaged beam for fast computation.
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Dissertations / Theses on the topic "Natural frequencies of free vibration"

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Mochida, Yusuke. "Bounded Eigenvalues of Fully Clamped and Completely Free Rectangular Plates." The University of Waikato, 2007. http://hdl.handle.net/10289/2508.

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Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.
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Shih, Hoi Wai. "Damage assessment in structures using vibration characteristics." Queensland University of Technology, 2009. http://eprints.qut.edu.au/30319/.

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Changes in load characteristics, deterioration with age, environmental influences and random actions may cause local or global damage in structures, especially in bridges, which are designed for long life spans. Continuous health monitoring of structures will enable the early identification of distress and allow appropriate retrofitting in order to avoid failure or collapse of the structures. In recent times, structural health monitoring (SHM) has attracted much attention in both research and development. Local and global methods of damage assessment using the monitored information are an integral part of SHM techniques. In the local case, the assessment of the state of a structure is done either by direct visual inspection or using experimental techniques such as acoustic emission, ultrasonic, magnetic particle inspection, radiography and eddy current. A characteristic of all these techniques is that their application requires a prior localization of the damaged zones. The limitations of the local methodologies can be overcome by using vibration-based methods, which give a global damage assessment. The vibration-based damage detection methods use measured changes in dynamic characteristics to evaluate changes in physical properties that may indicate structural damage or degradation. The basic idea is that modal parameters (notably frequencies, mode shapes, and modal damping) are functions of the physical properties of the structure (mass, damping, and stiffness). Changes in the physical properties will therefore cause changes in the modal properties. Any reduction in structural stiffness and increase in damping in the structure may indicate structural damage. This research uses the variations in vibration parameters to develop a multi-criteria method for damage assessment. It incorporates the changes in natural frequencies, modal flexibility and modal strain energy to locate damage in the main load bearing elements in bridge structures such as beams, slabs and trusses and simple bridges involving these elements. Dynamic computer simulation techniques are used to develop and apply the multi-criteria procedure under different damage scenarios. The effectiveness of the procedure is demonstrated through numerical examples. Results show that the proposed method incorporating modal flexibility and modal strain energy changes is competent in damage assessment in the structures treated herein.
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Mazzochi, Rudimar. "Elementos finitos quadrilaterais Hermitianos de alta regularidade gerados pela partição de unidade aplicados na solução de problemas de elasticidade e elastodinâmica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/96314.

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Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori.<br>In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.
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Menezes, Joao Carlos. "Natural frequencies of thin cylindrical vessels filled with liquids." Thesis, University of Liverpool, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.291956.

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Gupta, Shakti Singh. "Elastic constants from molecular mechanics simulations of frequencies of free-free single-walled carbon nanotubes and clamped single-layer graphene sheets." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/27576.

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Elastic constants of single-walled carbon nanotubes (SWCNTs) and single-layer graphene sheets (SLGSs) are determined by studying their free vibration characteristics using molecular mechanics (MM) simulations with the MM3 potential and finding their equivalent continuum structures (ECSs). The computational framework has been validated by comparing the presently computed basal plane stiffness and frequencies of radial breathing modes (RBMs) with those available in the literature. We have considered armchair, zigzag and chiral SWCNTs of aspect ratios (length/ diameter in the unloaded relaxed configuration) ranging from 2 to 15. The wall thickness of ECSs of SWCNTs is determined by applying continuum theories, viz., beam, shell and 3D-linear elasticity to ECSs and equating their frequencies with those of SWCNTs obtained from the MM simulations. An expression for the wall thickness of an ECS of a SWCNT in terms of its chiral indices is deduced. The wall thickness of an ECS of a SWCNT is found to increase with an increase in its radius and to saturate at 1.37 Ã for the radius exceeding 15 Ã . Poissonâ s ratio for zigzag SWCNTs decreses with an increase in the tube radius, but that for armchair SWCNTs exhibits the opposite trend. For the same radius, Poissonâ s ratio of a chiral SWCNT is slightly more than that for an armchair tube but a little less than that for a zigzag tube. For zigzag SWCNTs, frequencies of inextensional modes of vibration saturate with an increase in the circumferential wave number but those of their ECSs do not. The MM simulations of uniaxial tensile deformations of SLGSs of aspect ratios (length/width) ~ 10 give the basal plane stiffness of ~ 340 N/m. The MM simulations of free vibrations of clamped SLGSs and the analysis of vibrations of their ECSs with a continuum theory gives a wall thickness of ~ 1 Ã for a SLGS.<br>Ph. D.
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Bean, Jaco. "Vibration characterization of an active magnetic bearing supported rotor / J. Bean." Thesis, North-West University, 2011. http://hdl.handle.net/10394/7029.

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The McTronX Research group at the Potchefstroom campus of the North-West University, aims to establish a knowledge base on active magnetic bearing (AMB) systems. Up to date, the group has established a firm knowledge base on various topics related to AMB systems. A recent focus was the design and development of a high speed AMB supported rotor system called the rotor delevitation system (RDS) to analyse rotor drops. During the testing phase of the RDS, the machine exhibited vibrations, of which the origins were unknown. The research presented in this dissertation sets out to characterize the vibrations of the RDS, which is the group’s first attempt to fulfil the need for characterizing vibrations in an AMB supported rotor. Emphasis is placed on characterizing the natural response of the RDS rotor, stator and integrated system. The research project is defined in terms of four main objectives: rotor and stator characterization, modelling, system characterization and rotor dynamic diagnostics. A comprehensive literature study introduces the fundamental concepts regarding vibrations of single and multiple degree of freedom systems. These concepts include; natural frequencies, damping, machine vibrations, rotor dynamics and modelling techniques. These modelling techniques are introduced to verify the experimental methodology used to determine the natural frequencies. A critical overview of the literature contextualises the theory with the research investigation. For the RDS rotor and stator characterization, a modal analysis process also known as the “bump test” is implemented in order to validate the bending natural frequencies of the rotor and stator. A simulation model of the RDS is constructed in the finite element (FE) package DyRoBeS®. The model is verified with a numerical and an analytical model and validated with the measured bending natural frequencies of the RDS rotor. For the system characterization, a number of modal analysis processes are implemented, which validates the rigid body natural frequencies of the RDS. These frequencies are also used to validate the FE simulation. The origins of the synchronous vibration harmonics are verified by formulating and evaluating hypotheses according to different modal analysis processes. From the RDS rotor modal analysis it was identified that a bending natural frequency of the rotor is situated at approximately 443.33 Hz. This was verified using the FE simulation model. During the system modal analyses, it was identified that only one rigid body natural frequency, situated at approximately 62 Hz, is excited. This frequency increases with the differential gain control parameter of the system up to approximately 140 Hz. After evaluating two hypotheses regarding the origins of the synchronous vibrations harmonics, it was verified that non-circularity of the rotor at the measuring positions is the cause. Overall the objectives of the study were addressed by characterizing the natural frequencies of the rotor, stator and RDS system. This include the mode forms of the rigid body and bending natural frequencies of the system. The results of the verification and validation methods correlated, which imply these methods are reliable to identify the origins of vibrations in rotor-bearing systems. The differential gain control parameter of the AMBs control the equivalent damping in the RDS. An increase in this parameter should lead to a decrease in amplitude and frequency of the maximum vibration, and vice versa. However, it was noted that an increase in this parameter caused a linear increase in the rigid body natural frequency. The literature indicates that this effect can only be caused by an increase in system stiffness. It is therefore recommended to evaluate the stiffness of the system as a function of the differential gain control parameter.<br>Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012.
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Zdunek, Agnieszka Izabela. "Prediction of natural frequencies of turbine blades for turbocharger application : an investigation of the finite element method, mathematical modelling and frequency survey methods applied to turbocharger blade vibration in order to predict natural frequencies of turbocharger blades." Thesis, University of Bradford, 2014. http://hdl.handle.net/10454/7328.

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Methods of determining natural frequencies of the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs for various environmental conditions were investigated by application of Finite Element Analysis and beam theory. Modelling and simulation methods were developed ; the first method composed of 15 finite element simulations ; the second composed of 15 finite element simulations and a set of experimental frequency survey results; the third composed of 5 simulations , an incorporated mathematical model and a set of experimental frequency survey results. Each of these methods was designed to allow prediction of resonant frequency changes across a range of exhaust gas temperature and shaft rotational speed. For the new modelling and simulation methods, an analysis template and a plotting tool were developed using Microsoft Excel and MATLAB software. A graph showing a frequency-temperature-speed variations and a Campbell Diagram that incorporates material stiffening and softening effects across a range of rotational speeds was designed, and applied to the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs. New design methodologies for turbine wheels were formulated and validated, showing a good agreement with a range of data points from frequency survey, strain-gauge telemetry and laser tip-timing test results. The results from the new design method were compared with existing single compensation factor methodology, and showed a great improvement in accuracy of prediction of modal vibration. A new nomenclature for the mode shapes of a turbocharger’s blade was proposed, designed and demonstrated to allow direct identification of associated mode shape. It is concluded that Finite Element Analysis combined with the frequency survey is capable of predicting changes in turbine natural frequencies and, when incorporated into the existing turbine design methodology, resulted in a major improvement in the accuracy of the predictions of vibration frequency.
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Sakanaka, Sandra Hiromi. "Determinação de frequencias naturais e cargas criticas em placas incluindo o efeito da deformação por cortante com o metodo dos elementos de contorno." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/257772.

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Orientador: Leandro Palermo Jr<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo<br>Made available in DSpace on 2018-08-09T15:27:34Z (GMT). No. of bitstreams: 1 Sakanaka_SandraHiromi_M.pdf: 2300706 bytes, checksum: bf530823f185b6dbee7f56dd83d01a67 (MD5) Previous issue date: 2006<br>Resumo: A análise de vibração livre e de instabilidade de placas finas e placas moderadamente espessas é apresentada através do método dos elementos de contorno (MEC) considerando o efeito da deformação pela força cortante e, particularmente para o cálculo de freqüências naturais, o efeito da inércia rotatória é também considerado. A formulação da solução fundamental é baseada na teoria de Mindlin (1951) mas resultados para a teoria de Kirchhoff (1850) também podem ser obtidos [Palermo Jr. (2000)]. O presente trabalho usa a técnica da iteração inversa através do coeficiente de Rayleigh para a determinação das menores freqüências naturais e cargas críticas de instabilidade das placas. A implementação numérica emprega elementos de contorno isoparamétricos lineares contínuos e descontínuos. Elementos constantes de domínio são usados. Os parâmetros nodais são posicionados nos extremos dos elementos e os pontos de carregamento dos elementos descontínuos são deslocados para o interior a uma distância igual a um quarto do comprimento do elemento. Expressões analíticas das integrais de contorno são desenvolvidas para os casos em que o elemento contém o ponto de carregamento e integração numérica de Gauss-Legendre é feita nos outros casos. As integrais de domínio foram transformadas em integrais de contorno para cada célula e foram tratadas como cargas de superfície atualizadas através de um processo iterativo. Os resultados obtidos foram comparados com valores encontrados na literatura para demonstrar a precisão do presente trabalho<br>Abstract: Free-vibration analysis and static buckling loads analysis of thin and thick plates considering the shear deformation effects using the Boundary Element Method (BEM) is presented. For the calculation of natural frequencies, the rotatory inertia is also counted. The formulation of the fundamental solution considers Mindlin¿s plates but results according to the classic theory can also be obtained [Palermo Jr. (2000)]. The present article makes use of the inverse iteration with Rayleigh coefficient to determine the smallest natural frequencies and the smallest static buckling loads of the plates. The numerical implementation employed continuous or discontinuous isoparametric linear boundary elements according to the characteristics of the problem to be solved. Constant domain elements are used. Nodal parameters have been placed at the ends of the elements and the source point of the discontinuous elements were positioned at a distance equal to one quarter of the element length. Analytical expressions have been employed in the integration on elements containing the source point and Gauss-Legendre numerical integration scheme otherwise. The domain integrals containing the inertia effects or nonlinear effect have been transformed into boundary integrals for each cell and were treated as surface loads updated in an iterative process. The obtained results were compared to those in literature to demonstrate the precision of this proposal<br>Mestrado<br>Estruturas<br>Mestre em Engenharia Civil
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Lovejoy, Andrew Elwyn. "Natural frequencies and an atlas of mode shapes for generally-laminated, thick, skew, trapezoidal plates." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06102009-063206/.

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Jacobsen, Erica Dawn. "Forced Vibration Testing and Analysis of Pre- and Post- Retrofit Buildings." DigitalCommons@CalPoly, 2011. https://digitalcommons.calpoly.edu/theses/531.

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ABSTRACT Forced Vibration Testing and Analysis of Pre- and Post- Retrofit Buildings Erica Dawn Jacobsen The primary goal of the thesis was to detect the retrofit through vibration testing of both buildings. The secondary goal focused on correctly identifying the behavior of the building through FVT, comparing that behavior to computational model predictions, and determining the necessary level of detail to include in the computational modeling. Forced vibration testing (FVT) of two stiff-wall/flexible-diaphragm buildings yielded natural frequencies and mode shapes for the two buildings. The buildings were nearly identical with the exception that one had been retrofitted. Both buildings were comprised of concrete shearwalls and steel moment frames in the north/south direction and moment frames in the east/west direction. The retrofit strengthened the moment connections and added braces to the perimeter walls in the east/west direction. The natural frequencies were found through FVT by setting a 30-lb shaker on the roof of both buildings and sweeping through a range of frequencies in both the east/west and north/south directions. Accelerometers were placed on the building to detect the accelerations. The peaks on the Fast Fourier Transform (FFT) graphs indicated the frequencies at which the structure resonated. Mode shapes were tested for by placing the shaker in a position ideal for exciting the mode and setting the shaker to the natural frequency detected from the FFT graphs. The accelerometers were placed around the roof of the building to record the mode shape. After testing, computational models were created to determine if the models could accurately predict the frequencies and mode shapes of the buildings as well as the effect of the retrofit. A series of increasingly complex computational models, ranging from hand calculations to 3D models, were created to determine the level of detail necessary to predict the building behavior. Natural frequencies were the primary criteria used to determine whether the model accurately predicted the building behavior. The mid-diaphragm deflection and base shear from spectral analysis were the final criteria used to compare these select models. It was determined that in order to properly capture the modal behavior of the building, the sawtooth framing, major beams, and the lateral-force-resisting-system (LFRS) must be modeled. Though the mode shape of the building is dominated by the flexible diaphragm, the LFRS is necessary to model to accurately predict both the natural frequency of the building as well as the diaphragm deflection.
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Books on the topic "Natural frequencies of free vibration"

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Wu, K. Chauncey. Free vibration of hexagonal panels simply supported at discrete points. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Gotsis, Pascal K. Laminated thin shell structures subjected to free vibration in a hygrothermal environment. National Aeronautics and Space Administration, 1994.

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Gotsis, Pascal K. Laminated thin shell structures subjected to free vibration in a hygrothermal environment. National Aeronautics and Space Administration, 1994.

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Canada. Defence Research Establishment Atlantic. Prediction of the Strength and Natural Frequencies of Vibration of Cfav Question Propellers Nrc 45 and Nsmb 5363. s.n, 1985.

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Stredulinsky, David C. The prediction of strength and natural frequencies of vibration of a model submarine propeller subjected to large centrifugal loads in a wind tunnel. Defence Research Establishment Atlantic, 1992.

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Free vibration of hexagonal panels simply supported at discrete points. National Aeronautics and Space Administration, Langley Research Center, 1991.

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A, Kolkailah Faysal, Elghandour Eltahry I, and United States. National Aeronautics and Space Administration., eds. Modal analysis of embedded passive damping materials in composite plates with different orientations: Final report for NASA-Dryden Flight Research Center, joint research interchange, May 1, 1997-July 24, 1998. National Aeronautics and Space Administration, 1998.

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A, Kolkailah Faysal, Elghandour Eltahry I, and United States. National Aeronautics and Space Administration., eds. Modal analysis of embedded passive damping materials in composite plates with different orientations: Final report for NASA-Dryden Flight Research Center, joint research interchange, May 1, 1997-July 24, 1998. National Aeronautics and Space Administration, 1998.

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Center, Langley Research, ed. An analytical study of the effects of transverse shear deformation and anisotropy on natural vibration frequencies of laminated cylinders. National Aeronautics and Space Administration, Langley Research Center, 1988.

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Center, Langley Research, ed. An analytical study of the effects of transverse shear deformation and anisotropy on natural vibration frequencies of laminated cylinders. National Aeronautics and Space Administration, Langley Research Center, 1988.

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Book chapters on the topic "Natural frequencies of free vibration"

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Singh, Deepak Kumar, Priyaranjan Pal, and Shashi Kant Duggal. "Free Vibration Frequencies of Lock Gate Structure." In Lecture Notes in Civil Engineering. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5195-6_10.

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Mazzei, Arnaldo J., and Richard A. Scott. "Natural Frequencies of Layered Beams Using a Continuous Variation Model." In Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15233-2_20.

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Reichl, Katherine K., and Daniel J. Inman. "Constant Mass Metastructure with Vibration Absorbers of Linearly Varying Natural Frequencies." In Topics in Modal Analysis & Testing, Volume 10. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54810-4_16.

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Hino, Junichi, Satoshi Ooya, and Yuka Shigenai. "Estimation of Normalized Eigenmodes and Natural Frequencies by Using the Effect of Accelerometers Mass." In Vibration Engineering for a Sustainable Future. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-48153-7_23.

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Georgas, P., and G. S. Schajer. "Simultaneous Measurement of Plate Natural Frequencies and Vibration Mode Shapes Using ESPI." In Conference Proceedings of the Society for Experimental Mechanics Series. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4235-6_10.

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Elishakoff, Isaac. "Random Vibration of System with Finitely Many Degrees of Freedom and Several Coalescent Natural Frequencies." In Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40394-2_2.

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Zelmat, Yassine. "Numerical Investigation on the Effects of Natural Frequencies of Vibration Uncertainties on the Maximum Seismic Response." In Sustainability and Automation in Smart Constructions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35533-3_38.

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Williams, K. R., and T. H. J. Lesser. "A Finite Element Analysis of the Natural Frequencies of Vibration of the Human Tympanic Membrane. Part II." In Proceedings of the First International Conference on Interfaces in Medicine and Mechanics. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-011-7477-0_29.

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Kim, Yoon Hyuk, Chang Hwan Byun, and Taek Yul Oh. "Effect of Osteoporosis on Natural Frequencies in Mouse Femur: Vibration Test and Micro-CT Based Finite Element Analysis." In Experimental Mechanics in Nano and Biotechnology. Trans Tech Publications Ltd., 2006. http://dx.doi.org/10.4028/0-87849-415-4.851.

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Almendros, Javier, Francisco Luzón, and Antonio Posadas. "Microtremor Analyses at Teide Volcano (Canary Islands, Spain): Assessment of Natural Frequencies of Vibration Using Time-dependent Horizontal-to-vertical Spectral Ratios." In Geodetic and Geophysical Effects Associated with Seismic and Volcanic Hazards. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7897-5_18.

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Conference papers on the topic "Natural frequencies of free vibration"

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Pentaras, Demetris, and Isaac Elishakoff. "Free Vibration of the Triple-Walled Carbon Nanotubes." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10265.

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Natural frequencies of the triple-walled carbon nanotubes (TWCNTs) are determined both exactly and approximately. For the case of TWCNT which is simply supported at it ends closed-form solutions are obtained. It is shown that there are three series of natural frequencies corresponding to the cubic polynomial equation for natural frequency squares. For the TWCNT that has other boundary conditions approximate Bubnov-Galerkin and Petrov-Galerkin methods are applied. Simple polynomial coordinate functions are utilized. Each of these methods yields three natural frequencies corresponding to the lower and of each frequency spectra.
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Hamidzadeh, Hamid R. "Free Transverse Vibration of Thin Rotating Disks: Nonlinear Analysis." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81491.

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An analytical method is adopted to determine natural frequencies for a nonlinear spinning disk. The disk is assumed to be isotropic and rotating under steady state conditions. The effects of amplitude and rotating speed on natural frequencies are determined. The developed procedure is also capable of analyzing natural frequencies of linear free vibration, which is independent of amplitude. Attention is confined to determine natural frequencies for different numbers of nodal diameters. The developed procedure does not consider modes of vibration corresponding to nodal circles. Validity of this procedure is verified by comparing some of the computed results with those established for certain cases.
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He, Xiaocong, Ian Pearson, and Ken Young. "Free Vibration Characteristics of SPR Joints." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95219.

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Self-piercing riveting (SPR) has drawn more attention in recent years because it can join some advanced materials that are hard to weld, such as aluminum alloy sheets. In this paper, the free torsional vibration characteristics of single lap-jointed encastre SPR beam are investigated in detail. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of the single lap-jointed encastre SPR beam of different characteristics of sheets to be jointed. Numerical examples show that the torsional natural frequencies increase significantly as the Young’s modulus of the sheets increase, but almost no change corresponding to the change in Poisson’s ratio of the sheets to be joint. The mode shapes show that there are different deformations in the jointed section of SPR beam compared with the reference encastre beam without joint. These different deformations may cause different natural frequency values and different stress distributions.
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Hamidzadeh, H. R., and M. Dehghani. "Linear In-Plane Free Vibration of a Rotating Disk." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8146.

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Abstract This paper discusses linear in-plane free vibration of a homogeneous, isotropic, linear visco-elastic rotating disk. Two-dimensional theory of elastico-dynamic is employed to develop the general governing equations of motion. In this analysis, a constant angular velocity is assumed. The wave equations and Bessel Functions of the first and second kind are utilized to obtain the natural frequencies. Natural frequencies are found for a number of modes with several clamping ratios. These natural frequencies were compared with the available established results. Also, the influence of rotational speed and clamping ratio on the natural frequencies and the mode shapes of vibration are determined. The analysis provides information about the elastic stability of the rotating disks for several modes of vibration.
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Shiau, L. C., and S. T. Hwang. "Free Vibration of Rectangular Composite Laminates With Delamination." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43036.

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In this paper, the effect of delamination on natural frequencies and natural modes of a simply supported rectangular symmetric composite plate with through-width delamination was investigated by the finite strip method. The delamination was assumed to be located at mid-plane of the laminate so that the contact/impact phenomenon between delaminated interfaces does not exist for the free vibration of the laminate. A finite strip with bending and in-plane stiffnesses was derived for the free vibration analysis. The effects of delamination length, delamination location, fiber angle, stacking sequence, and aspect ratio of the laminate on the natural frequencies of the laminate were studied and presented. Results show that the above mentioned factors have considerable effect on the natural frequencies of the laminate. The aspect ratio of the plate is also having significant effect on the frequency of the laminates, especially on the mode 2 frequency of the cross-ply laminate.
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Song, Xiaolei, and Haijun Liu. "Free Vibration of Bistable Clamped-Clamped Beams: A Preliminary Study." In ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/detc2020-22560.

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Abstract We present a preliminary study on bistable clamped-clamped beams both analytically and experimentally relating the linear post-buckling vibrations to the generated sound. In the analytical study, closed-form natural frequencies and mode shapes around the first buckled configuration are derived from an eigenvalue problem. It is found that as the static deflection of the buckled beam increases, the natural frequencies of the anti-symmetric vibrational modes stay constant, while those of the symmetric vibrational modes increase asymptotically. In the experimental study, a bistable clamped-clamped buckled beam made of steel is switched quasi-statically by hand between the two stable configurations. The generated sound is measured by a microphone and analyzed in both temporal and frequency domains, which agrees well with the analytical results. This work lays the foundation for using bistable beams in a variety of applications such as actuators, resonators, energy harvesters, and vibration reduction.
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Moxey, L., and H. Hamidzadeh. "Free Vibration of a Thin-Film Inflated Torus." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42491.

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In this paper an overview of the mathematical model for an inflated thin-film toroidal structure is provided. In particular, attention has been confined to determine the free vibrations of inflated circular toroidal members. The provided solution is based on an improved set of equations of motion for uniform membrane. From which the dependence of natural frequencies on material properties, dimension, mode of vibration, and the inner pressure can be investigated. The validity of the developed models was verified by comparing some of the computed results with those available for special cases. Numerical results for natural frequencies and mode shapes are provided for a specific thin-film inflated torus.
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Cao, D. Q., M. T. Song, and W. D. Zhu. "Modeling and Free Vibration Analysis of a Complex Cable-Stayed Bridge." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70555.

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A complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern the motions of the cables and segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge, which includes both the transverse and longitudinal vibrations of the cables, are determined. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for a symmetrical case with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies and localized mode shapes.
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Joubaneh, E. F., and O. R. Barry. "On the Free Vibration Analysis of a Sandwich Beam With Tip Mass." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87535.

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This paper presents the free vibration analysis of a sandwich beam with a tip mass using higher order sandwich panel theory (HSAPT). The governing equations of motion and boundary conditions are obtained using Hamilton’s principle. General Differential Quadrature (GDQ) is employed to solve the system governing equations of motion. The natural frequencies and mode shapes of the system are presented and Ansys simulation is performed to validate the results. Various boundary conditions are also employed to examine the natural frequencies of the sandwich beam without tip mass and the results are compared with those found in the literature. Parametric studies are conducted to examine the effect of key design parameters on the natural frequencies of the sandwich beam with and without tip mass.
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Pan, Luyan, Xiang Zhu, Tianyun Li, Yueyang Han, and Xiaotian Liang. "Vibration Analysis of a Horizontal Partially Fluid-Filled Cylindrical Shell Considering Sloshing Effect of Free Surface." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-12263.

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Abstract The free and forced vibrations of a horizontal partially fluid-filled cylindrical shell with sloshing effect are studied based on the finite element method. The structure and inner fluid taking into account the sloshing effect of the free surface are simulated by the shell and acoustic elements respectively. The natural frequencies of sloshing fluid and shell structure are calculated simultaneously by the FEM. To verify the accuracy of the results, the shell’s natural frequencies are compared with published results. The effects of the structural parameters and fluid depth on the vibration of the coupled system are discussed. The natural frequencies of a sloshing fluid can be divided into low-frequency and high-frequency part, and the low-frequency part refers to the pressure fluctuation caused by the sloshing of the free surface, while the high-frequency part corresponds to the pressure fluctuation of the particles below the free surface. The thinner the shell thickness is, the lower the sloshing frequency of free surface and coupled modal frequency of the shell are. With the increase of the liquid depth, the natural sloshing frequency of the free surface increases slightly while the coupled modal frequency of the shell decreases. The impact of the free surface effect on the coupled vibration cannot be omitted when the shell’s natural frequencies are close to the sloshing frequencies.
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