Journal articles: 'Clamped plate vibration'

1

Lal, Roshan, and Renu Saini. "Mode shapes and frequencies of thin rectangular plates with arbitrarily varying non-homogeneity along two concurrent edges." Journal of Vibration and Control 23, no. 17 (January 22, 2016): 2841–65. http://dx.doi.org/10.1177/1077546315623710.

Full text

Abstract:

Analysis and numerical results are presented for free transverse vibrations of isotropic rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges on the basis of Kirchhoff plate theory. For the non-homogeneity, a general type of variation for Young’s modulus and density of the plate material has been assumed. Generalized differential quadrature method has been used to obtain the eigenvalue problem for such model of plates for four different combinations of boundary conditions at the edges namely, (i) fully clamped, (ii) two opposite edges are clamped and other two are simply supported, (iii) two opposite edges are clamped and other two are free, and (iv) two opposite edges are simply supported and other two are free. By solving these eigenvalue problems using software MATLAB, the lowest three eigenvalues have been reported as the first three natural frequencies for the first three modes of vibration. The effect of various plate parameters on the vibration characteristics has been analysed. Three dimensional mode shapes have been plotted. A comparison of results with those available in literature has been presented.

APA, Harvard, Vancouver, ISO, and other styles

2

Eisenberger, Moshe, and Aharon Deutsch. "Static Analysis for Exact Vibration Analysis of Clamped Plates." International Journal of Structural Stability and Dynamics 15, no. 08 (October 29, 2015): 1540030. http://dx.doi.org/10.1142/s0219455415400301.

Full text

Abstract:

Presented herein is a new method for the analysis of plates with clamped edges. The solutions for the natural frequencies of the plates are found using static analysis. The starting are the equations of motion of an isotropic rectangular plate supported on Winkler elastic foundation, with a positive or negative value. In either case, one can solve the displacements of such a plate under a given concentrated load. This deflection will be infinite if the plate losses its stiffness, or in other words, the generalized foundation is causing the plate to be unstable. The solution for the vibration frequencies of the plate is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load on the plate. The solution for a clamped plate is decomposed as the sum of three cases of plates resting on elastic foundation: simply supported plate with a concentrated load, and two cases of distributed moments along opposite edges. The solution for simply supported plates with elastic foundation is found using Navier's method. For zero force, the vibration frequencies are found up to the desired accuracy by careful calculations at the neighborhood of the roots.

APA, Harvard, Vancouver, ISO, and other styles

3

Tseng, J. G., and J. A. Wickert. "Vibration of an Eccentrically Clamped Annular Plate." Journal of Vibration and Acoustics 116, no. 2 (April 1, 1994): 155–60. http://dx.doi.org/10.1115/1.2930406.

Full text

Abstract:

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.

APA, Harvard, Vancouver, ISO, and other styles

4

Liew, K. M. "Vibration of Clamped Circular Symmetric Laminates." Journal of Vibration and Acoustics 116, no. 2 (April 1, 1994): 141–45. http://dx.doi.org/10.1115/1.2930404.

Full text

Abstract:

Treated in this paper is the free-flexural vibration analysis of symmetrically laminated thin circular plates. The total energy functional for the laminated plates is formulated where the pb-2 Ritz method is applied for the solution. The assumed displacement is defined as the product of (1) a two-dimensional complete polynomial function and (2) a basic boundary function. The simplicity and accuracy of the numerical procedure will be demonstrated by solving some plate examples. In the present study, the effects of material properties, number of layers and fiber stacking sequences upon the vibration frequency parameters are investigated. Selected mode shapes by means of contour plots for several 16-ply laminated plates with different fiber stacking sequences and composite materials are presented. This study may provide valuable information for researchers and engineers in design applications. In addition, the present solution plays an important role in increasing the existing data base for future references.

APA, Harvard, Vancouver, ISO, and other styles

5

MARETIC, RATKO, and VALENTIN GLAVARDANOV. "VIBRATION OF CIRCULAR PLATE WITH AN INTERNAL ELASTIC RING SUPPORT UNDER EXTERIOR EDGE PRESSURE." International Journal of Structural Stability and Dynamics 14, no. 01 (December 17, 2013): 1350053. http://dx.doi.org/10.1142/s0219455413500533.

Full text

Abstract:

In this paper, we analyze the transverse vibration of a circular plate loaded by uniform pressure along its edge. The plate is supported by an elastic ring support being coaxial with the plate. At its edge the plate is clamped but the radial displacement is allowed. Apart from this problem, the heated plate clamped at its edge, but without the possibility of radial displacement, is also analyzed. The analytical solution of governing equation is obtained in the form of Bessel's functions. Using the analytical solution, the frequencies of transverse vibrations depending on loads, elastic ring stiffness and the location of ring are obtained. The results show that the lowest frequencies vibrations can be either symmetric or asymmetric having one or two nodal diameters. It is also shown that multiple vibration frequencies can occur for special values of load and ring stiffness.

APA, Harvard, Vancouver, ISO, and other styles

6

Tu, Jian Xin, Zhi Ren Wang, Han Zhu, and Ping Wang. "The Nonlinear Random Vibration of a Clamped Rectangular Thin Plate in Magnetic Field." Applied Mechanics and Materials 628 (September 2014): 127–32. http://dx.doi.org/10.4028/www.scientific.net/amm.628.127.

Full text

Abstract:

In this paper, the magneto-elastic nonlinear random vibration of a clamped rectangular thin plate in magnetic field is studied. According to the magneto-elastic theory of plates and shells and the theory of structural random vibration, the magneto-elastic nonlinear random vibration equation of a clamped rectangular thin plate in a magnetic field is derived. Then the nonlinear random vibration equation is transferred into the Ito differential equation, and the Ito differential equation is solved using FPK equation method. Thus the numerical characteristics of displacement response and velocity response of the rectangular thin plate are obtained. Finally, through a numerical example, the influences of magnetic field parameters on the numerical characteristics are discussed, and some methods which can be used to effectively control the random vibration responses of the plate are given.

APA, Harvard, Vancouver, ISO, and other styles

7

Shi, Jian Wei, Akihiro Nakatani, and Hiroshi Kitagawa. "Vibration analysis of fully clamped arbitrarily laminated plate." Composite Structures 63, no. 1 (January 2004): 115–22. http://dx.doi.org/10.1016/s0263-8223(03)00138-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Grover, D. "Damping in thin circular viscothermoelastic plate resonators." Canadian Journal of Physics 93, no. 12 (December 2015): 1597–605. http://dx.doi.org/10.1139/cjp-2014-0575.

Full text

Abstract:

The governing equations of transverse motion and heat conduction of a homogenous, isotropic, thermally conducting, Kelvin–Voigt-type medium, based on Kirchhoff–Love plate theory, are established for out-of-plane vibrations of a generalized viscothermoelastic circular thin plate. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized and coupled viscothermoelastic plates. It is noticed that the damping of vibrations significantly depends on mechanical relaxation times and thermal relaxation time in addition to thermomechanical coupling in a circular plate under resonance conditions. The surface conditions also impose significant effects on the vibrations of such resonators. The numerical results may also be illustrated in the case of a circular plate and an axisymmetric circular plate for clamped and simply supported boundary conditions for fixed aspect ratio, fixed radius, and fixed thickness, respectively.

APA, Harvard, Vancouver, ISO, and other styles

9

Hosokawa, K., Y. Yamada, and T. Sakata. "Free-Vibration Analysis of Clamped Antisymmetrically Laminated Elliptical Plates." Journal of Applied Mechanics 65, no. 2 (June 1, 1998): 341–45. http://dx.doi.org/10.1115/1.2789060.

Full text

Abstract:

In a previous paper, a numerical approach for analyzing the free vibration problem of an unsymmetrically laminated fiber-reinforced plastic composite plate was proposed by the authors. In the present paper, this approach is applied to the clamped antisymmetrically laminated elliptical plate. As numerical examples, the natural frequencies and the mode shapes of the circular and elliptical plates are estimated. The effects of the fiber orientation angle on natural frequency and mode shape are studied. Furthermore, the vibration tests of the clamped antisymmetrically laminated circular and elliptical plates made of carbon fiber-reinforced plastic are carried out, and the experimental natural frequency and mode shape are compared with the numerical results.

APA, Harvard, Vancouver, ISO, and other styles

10

Wu, Jiu Hui, A. Q. Liu, and H. L. Chen. "Exact Solutions for Free-Vibration Analysis of Rectangular Plates Using Bessel Functions." Journal of Applied Mechanics 74, no. 6 (April 23, 2005): 1247–51. http://dx.doi.org/10.1115/1.2744043.

Full text

Abstract:

A novel Bessel function method is proposed to obtain the exact solutions for the free-vibration analysis of rectangular thin plates with three edge conditions: (i) fully simply supported; (ii) fully clamped, and (iii) two opposite edges simply supported and the other two edges clamped. Because Bessel functions satisfy the biharmonic differential equation of solid thin plate, the basic idea of the method is to superpose different Bessel functions to satisfy the edge conditions such that the governing differential equation and the boundary conditions of the thin plate are exactly satisfied. It is shown that the proposed method provides simple, direct, and highly accurate solutions for this family of problems. Examples are demonstrated by calculating the natural frequencies and the vibration modes for a square plate with all edges simply supported and clamped.

APA, Harvard, Vancouver, ISO, and other styles

11

Liew, K. M., and K. Y. Lam. "A Set of Orthogonal Plate Functions for Flexural Vibration of Regular Polygonal Plates." Journal of Vibration and Acoustics 113, no. 2 (April 1, 1991): 182–86. http://dx.doi.org/10.1115/1.2930167.

Full text

Abstract:

A computationally efficient and very accurate numerical method is proposed for vibration analysis of regular polygonal plates with any combinations of clamped, simply-supported and free boundary conditions. The method involves the use of two-dimensional orthogonal polynomials generated by the Gram-Schmidt recurrence procedure. For the cases of simply supported and fully clamped hexagonal and octagonal plates, the results obtained agreed very well with those existing in the literature. The frequencies and mode shapes for several hexagonal and octagonal plates subjected to mixed boundary conditions are also presented.

APA, Harvard, Vancouver, ISO, and other styles

12

Cunningham, Sean M., David A. Tanner, Seamus Clifford, Daniela Butan, and Mark Southern. "Effect of Perforations on Resonant Modes of Flat Circular Plates." Key Engineering Materials 865 (September 2020): 31–35. http://dx.doi.org/10.4028/www.scientific.net/kem.865.31.

Full text

Abstract:

The vibration of perforated plates is central to certain engineering applications, such asdroplet-on-demand, inject printing and aerosol generation. To the author’s knowledge, there is limitedpublished literature outlining the effect of perforations on the natural frequency of a flat circular plate.This paper aims to further the understanding in this field research, by determining analytically theeffect of perforations on the natural frequency of boundary clamped flat circular plate. The methodology of this paper outlines the development of a dynamic finite element (FE) model which accurately embodies the effect of perforations on the natural frequency of a boundary clamped flat circular plate using modal analysis. This dynamic FE model aids in optimising the vibrational mechanics of perforated plates for specific engineering applications. The finding from this analysis demonstrates that the published literature is less conservative when compared to the FE method in predicting the effect of perforations on the natural frequency of a boundary clamped flat circular plate. Published literature uses a numerical analysis which underestimates the effect of perforations on the natural frequency of a boundary clamped flat circular plate when compared to the FE analysis reported in this study.

APA, Harvard, Vancouver, ISO, and other styles

13

Lindsay, A. E., W. Hao, and A. J. Sommese. "Vibrations of thin plates with small clamped patches." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150474. http://dx.doi.org/10.1098/rspa.2015.0474.

Full text

Abstract:

Eigenvalues of fourth-order elliptic operators feature prominently in stability analysis of elastic structures. This paper considers out-of-plane modes of vibration of a thin elastic plate perforated by a collection of small clamped patches. As the radius of each patch shrinks to zero, a point constraint eigenvalue problem is derived in which each patch is replaced by a homogeneous Dirichlet condition at its centre. The limiting problem is consequently not the eigenvalue problem with no patches, but a new type of spectral problem. The discrepancy between the eigenvalues of the patch-free and point constraint problems is calculated. The dependence of the point constraint eigenvalues on the location(s) of clamping is studied numerically using techniques from numerical algebraic geometry. The vibrational frequencies are found to depend very sensitively on the number and centre(s) of the clamped patches. For a range of number of punctures, we find spatial clamping patterns that correspond to local maxima of the base vibrational frequency of the plate.

APA, Harvard, Vancouver, ISO, and other styles

14

Yu, S. D., and W. L. Cleghorn. "ACCURATE FREE VIBRATION ANALYSIS OF CLAMPED MINDLIN PLATES USING THE METHOD OF SUPERPOSITION." Transactions of the Canadian Society for Mechanical Engineering 17, no. 2 (June 1993): 243–55. http://dx.doi.org/10.1139/tcsme-1993-0015.

Full text

Abstract:

The method of superposition is further developed to analyze free flexural vibration of clamped rectangular Mindlin plates. Comparison of results given by Mindlin’s theory of plates with those previously obtained by Reissner’s theory has shown that the rotatory inertia does not significantly affect plate flexural vibration. Accurate eigenvalues are presented for a number of values of plate aspect ratio along with two representative values of thickness ratio.

APA, Harvard, Vancouver, ISO, and other styles

15

Gharaibeh, M. A., A. M. Obeidat, and M. H. Obaidat. "Numerical Investigation of the Free Vibration of Partially Clamped Rectangular Plates." International Journal of Applied Mechanics and Engineering 23, no. 2 (May 1, 2018): 385–400. http://dx.doi.org/10.2478/ijame-2018-0022.

Full text

Abstract:

Abstract This paper studies the free vibration characteristics of rectangular plates with partially clamped edges around the corners using the finite element method. ANSYS Parametric Design Language (APDL) was utilized to produce the finite element (FE) models and to run the analysis. The FE models were used to obtain the plate first natural frequency and mode shape. A comprehensive investigation of the effect of the plate geometric parameters and different boundary condition properties on the natural frequency and mode shapes is presented. The results showed that the vibration characteristics of the structure are greatly dependent on the plate size and the constraint properties.

APA, Harvard, Vancouver, ISO, and other styles

16

SHI, Jianwei, Akihiro NAKATANI, and Hiroshi KITAGAWA. "933 Vibration Analysis of Full-clamped Arbitrarily Laminated Plate." Proceedings of the JSME annual meeting 2003.1 (2003): 351–52. http://dx.doi.org/10.1299/jsmemecjo.2003.1.0_351.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Park, Chan Il. "Frequency equation for the in-plane vibration of a clamped circular plate." Journal of Sound and Vibration 313, no. 1-2 (June 2008): 325–33. http://dx.doi.org/10.1016/j.jsv.2007.11.034.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Sun, Yu Xin, Yan Jiang, and Jia Ling Yang. "Thermoelastic Damping of the Axisymmetric Vibration of Laminated Trilayered Circular Plate Resonators." Applied Mechanics and Materials 313-314 (March 2013): 600–603. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.600.

Full text

Abstract:

In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results.

APA, Harvard, Vancouver, ISO, and other styles

19

Liu, Wei, HaiLong Sun, and Qiang Zhao. "Free Vibration and Transmission Response Analysis for Torsional Vibration of Circular Annular Plate." Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 45, no. 3 (January 10, 2021): 631–38. http://dx.doi.org/10.1007/s40997-020-00420-2.

Full text

Abstract:

AbstractIn this paper, free vibration and transmission response for the torsional vibration of circular annular plate are presented. To the author’s knowledge, few studies can be found for the torsional vibration from wave standpoint. For this purpose, in this study, natural frequencies for the torsional vibration of annular plate with clamped–clamped and free–free boundaries are calculated. The natural frequencies obtained by wave approach are compared with those derived by the classical method. Furthermore, transmissibility curves of the periodic annular model and Fibonacci annular model are analyzed. The finite element simulations are carried out to verify the theoretical results. Finally, the influence of inner radius and length ratio on the transmission response is also discussed. The obtained results are useful for the torsional vibration reduction of machinery structures.

APA, Harvard, Vancouver, ISO, and other styles

20

Gharaibeh, Mohammad A., and Amr M. Obeidat. "Vibrations Analysis of Rectangular Plates with Clamped Corners." Open Engineering 8, no. 1 (September 2, 2018): 275–83. http://dx.doi.org/10.1515/eng-2018-0030.

Full text

Abstract:

AbstractThis paper discusses the fundamental natural frequency of a thin elastic rectangular, isotropic and orthotropic, plates with clamped corners. Rayleigh’s method was used to analytically calculate the plate lowest natural frequency. In this solution, the vibration mode shape was assumed in a form that certifies the displacement as well as the rotational boundary conditions of the current problem. Finally, this paper provides useful information for evaluating the natural frequency of a plate with fixed corners with different mass attachments configurations.

APA, Harvard, Vancouver, ISO, and other styles

21

Kodhanda, Adarsh, Nisar Ali, Mahesh M. Sucheendran, and SE Talole. "Robust control of nonlinear resonance in a clamped rectangular plate." Journal of Vibration and Control 24, no. 18 (July 21, 2017): 4176–94. http://dx.doi.org/10.1177/1077546317721419.

Full text

Abstract:

This work is concerned with the control of nonlinear oscillations and resonance in a thin rectangular clamped plate representative of an aircraft panel with forcing frequency near to that of the first linear mode. The response of the plate to unsteady pressure force is modeled using the nonlinear von Kármán plate equation, the solution of which is obtained using modal expansion with the linear eigen modes. To suppress the vibrations, an input–output linearization (IOL) and uncertainty and disturbance estimator (UDE) based robust active vibration controller are proposed. The UDE is employed to estimate the composite uncertainty that comprises the effects of system nonlinearities and external disturbances and the estimate is used to augment the IOL controller to achieve robustness. The resulting controller, however, requires output derivatives for its implementation and to address the issue, an observer that employs the UDE estimated uncertainties for robustness is designed. Closed-loop stability for the overall system is established using Lyapunov’s direct method. The notable feature of the proposed design is that it neither requires an accurate plant model nor any detailed information about the external disturbances. Also, the design needs only the measurement of the center displacement of the plate for its implementation. Simulations are carried out for different disturbances and the results are presented to demonstrate the efficacy of the proposed controller. Lastly, performance comparison with some existing vibration control designs is carried out to showcase the effectiveness of the proposed formulation.

APA, Harvard, Vancouver, ISO, and other styles

22

Lal, R., and Yajuvindra Kumar. "Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation." Shock and Vibration 19, no. 3 (2012): 349–64. http://dx.doi.org/10.1155/2012/694746.

Full text

Abstract:

The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.

APA, Harvard, Vancouver, ISO, and other styles

23

Aridogan, Ugur, Ipek Basdogan, and Alper Erturk. "Random vibration energy harvesting on thin plates using multiple piezopatches." Journal of Intelligent Material Systems and Structures 27, no. 20 (July 28, 2016): 2744–56. http://dx.doi.org/10.1177/1045389x16635846.

Full text

Abstract:

Vibrational energy harvesting using piezoelectric cantilever beams has received significant attention over the past decade. When compared to piezoelectric cantilever-based harvesters, piezopatch energy harvesters integrated on plate-like thin structures can be a more efficient and compact option to supply electrical power for wireless structural health and condition monitoring systems. In this article, electroelastic modeling, analytical and numerical solutions, and experimental validations of piezopatch-based energy harvesting from stationary random vibrations of thin plates are presented. Electroelastic models for the series and parallel connected multiple piezopatches are given based on a distributed-parameter modeling approach for a thin host plate excited by a transverse point force. The analytical and numerical solutions for the mean power output and the mean-square shunted vibration response are then derived. The experimental measurements are carried out by employing a fully clamped thin plate with three piezopatches connected in series. It is shown that the analytical and numerical model predictions for the mean power output and the mean-square velocity response are in very good agreement with the experimental measurements. The electroelastic modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of piezoelectric energy harvesting from stationary random vibration of thin plates.

APA, Harvard, Vancouver, ISO, and other styles

24

Guo, X. X. "Vibration Characteristics of the Non-Conservative Thermoelastic Coupling Plate." Applied Mechanics and Materials 66-68 (July 2011): 551–56. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.551.

Full text

Abstract:

The vibration characteristics of the thermoelastic coupling rectangular plate under the action of uniformly distributed tangential follower force are investigated. The coupled thermoelastic differential equation of the plate under the action of uniformly distributed tangential follower force was derived. Dimensionless complex frequencies of the thermoelastic coupling rectangular plate with one edge clamped and other three edges simply supported, two opposite edges simply supported and other two edges clamped were calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor on the stability and critical load of the thin plate were analyzed. The results show that the flutter loads of the coupled modes increase with the increase of the dimensionless coupled thermoelastic factor and the aspect ratio.

APA, Harvard, Vancouver, ISO, and other styles

25

Cherepanov, Anatoliy. "FEATURES OF CALCULATION OF VIBRATIONS OF A PINCHED ROUND PLATE." Modern Technologies and Scientific and Technological Progress 1, no. 1 (May 17, 2021): 207–8. http://dx.doi.org/10.36629/2686-9896-2021-1-1-207-208.

Full text

Abstract:

A method for calculating the vibrations of a circular steel plate, clamped around the circumference and loaded with a short-term load, with the determination of the frequency of the fun damental tone (the lowest type of vibration), is considered. For practical calculations, the influence of the mass of the plate itself, as well as the mass of air or liquid, on the frequency of natural oscillations is taken into account.

APA, Harvard, Vancouver, ISO, and other styles

26

Gupta, A. K., and Anupam Khanna. "Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations." Shock and Vibration 15, no. 6 (2008): 713–23. http://dx.doi.org/10.1155/2008/873049.

Full text

Abstract:

Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

APA, Harvard, Vancouver, ISO, and other styles

27

Gupta, A. K., Harvinder Kaur, and Sanjay Kumar. "Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions." Shock and Vibration 17, no. 1 (2010): 93–105. http://dx.doi.org/10.1155/2010/716130.

Full text

Abstract:

The analysis presented here is to study the effect of thermal gradient on the vibration of visco-elastic rectangular plate (having clamped boundary condition on all the four edges) of variable thickness whose thickness varies parabolically in both directions. The effect of linear temperature variation has been considered. A frequency equation of plate has been obtained by Rayleigh-Ritz technique with two terms of deflection function. The assumption of small deflection and linear visco-elastic properties of ‘Kelvin’ type are taken. Deflection and time period corresponding to the first two modes of vibrations for clamped plate have been computed for various combinations of aspect ratio, thermal constants, and taper constants. Numerical computations have been performed for an alloy ‘Duralium’ and the results obtained are depicted graphically.

APA, Harvard, Vancouver, ISO, and other styles

28

Mahadevaswamy, P., and B. S. Suresh. "Influence of Aspect Ratio of Vibratory Flap on Dynamic Response of Clamped Rectangular Plate." International Journal of Structural Stability and Dynamics 15, no. 04 (May 2015): 1450064. http://dx.doi.org/10.1142/s0219455414500643.

Full text

Abstract:

The transverse vibration control of a clamped, rectangular, isotropic plate by a vibratory flap subjected to harmonic excitation has been investigated by Finite Element Analysis (FEA) and experimental technique. The vibratory flap is a new plate-type dynamic vibration absorber, which can vibrate on the plate when attached as a cantilever plate. The study has been focused specifically on the influence of aspect ratio of vibratory flap on the dynamic response of the plate at constant mass ratio and constant tuning frequency ratio. The study has revealed that the dynamic response of the plate varies with respect to the aspect ratio for aforementioned conditions. An optimum aspect ratio has also been obtained by minimizing the mass ratio with maximum attenuation in the first and second target frequencies. The results have shown that the optimized flap can trim down the plate vibrations by up to 90–95% in the fundamental mode. Moreover, the dynamic response of the plate can be improved to a great extent due to the adoption of an optimal aspect ratio of the flap. Finally, the experimental outcomes have shown fairly good agreement with the results obtained from the finite element analysis.

APA, Harvard, Vancouver, ISO, and other styles

29

Parnes, R. "Vibrations of Moderately Elliptic Clamped Plates: A Perturbation Scheme for Eigenvalues." Journal of Applied Mechanics 58, no. 3 (September 1, 1991): 724–28. http://dx.doi.org/10.1115/1.2897254.

Full text

Abstract:

Frequencies of vibration of an elliptic plate, clamped along the edge, are determined by means of a perturbation scheme based on a boundary perturbation method (B.P.M.). Eigenvalues are obtained corresponding to higher modes of vibration containing elliptic nodes, in addition to the fundamental mode. Comparison with previously derived values in the fundamental mode reveals that the present scheme leads to accurate results for moderately elliptic plates.

APA, Harvard, Vancouver, ISO, and other styles

30

Wu, Lei, and Lian Sheng Ma. "Thermal Vibration of Functionally Graded Circular Plates." Key Engineering Materials 353-358 (September 2007): 1777–80. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.1777.

Full text

Abstract:

Based on the nonlinear theory of von Karman plate, axisymmetric nonlinear vibration of a functionally graded circular plate with clamped boundary condition is investigated under thermal loading. It is assumed that the mechanical and thermal properties of functionally graded materials vary continuously through the thickness of the plate and obey a simple power law related to the volume fraction of the constituents. Motion equations for the problem are derived. Existence of harmonic vibrations is assumed and then Ritz-Kantorovich method is used to convert the dynamic Von Karman equations to a set of nonlinear ordinary differential equations. Finally a shooting method is employed to numerically solve the resulting differential equations. Effects of amplitude A, thermal load parameter λ and material constant n on the vibration behavior of FGM plate are discussed in details.

APA, Harvard, Vancouver, ISO, and other styles

31

Srivastava, A. K. L., P. K. Datta, and A. H. Sheikh. "Transverse Vibration of Stiffened Plates with Cutouts Subjected to In-Plane Uniform Edge Loading at the Plate Boundary." Shock and Vibration 11, no. 1 (2004): 9–19. http://dx.doi.org/10.1155/2004/891580.

Full text

Abstract:

Vibration characteristics of stiffened plates with cutouts subjected to uni-axial in-plane uniform edge loading at the plate boundaries are investigated using the finite element method. The characteristic equations for the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the equation of motion. The vibration frequencies and buckling load parameters for various modes of stiffened plates with cutouts have been determined for simply supported and clamped edge boundary conditions. In the structure modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. Numerical results are presented for a range of hole to plate width ratios of 0 to 0.8. The correlations of the natural frequencies and buckling parameters obtained by the present approach with those available in the literature are found to show good agreement.

APA, Harvard, Vancouver, ISO, and other styles

32

Nesterov, S. V. "Flexural vibration of a square plate clamped along its contour." Mechanics of Solids 46, no. 6 (December 2011): 946–51. http://dx.doi.org/10.3103/s0025654411060148.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

TAKENOUCHI, Ken, and Masaki SHIRATORI. "Axisymmetric Vibration of Clamped Circular Plate under Uniform Transverse Load." Proceedings of The Computational Mechanics Conference 2002.15 (2002): 239–40. http://dx.doi.org/10.1299/jsmecmd.2002.15.239.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Sharma, Ashish Kumar, Vandna, and Vijyeta Verma. "Mechanical Vibration of Orthotropic Square Plate with Clamped Boundary Conditions." Research Journal of Science and Technology 10, no. 4 (2018): 237. http://dx.doi.org/10.5958/2349-2988.2018.00034.7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Petzing, J. N., and J. R. Tyrer. "The effect of metallographic structure on clamped plate vibration characteristics." Experimental Mechanics 36, no. 2 (June 1996): 127–34. http://dx.doi.org/10.1007/bf02328708.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Yang, Yongqiang, Zhongmin Wang, and Yongqin Wang. "Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch." Journal of Low Frequency Noise, Vibration and Active Control 38, no. 2 (December 22, 2018): 558–73. http://dx.doi.org/10.1177/1461348418817465.

Full text

Abstract:

Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

APA, Harvard, Vancouver, ISO, and other styles

37

Zhao, Yong Gang, Wei Dong Zhao, Shi Rong Li, and Lian Sheng Ma. "Nonlinear Response of Clamped Circular Plates Subjected to Transverse Excitation Load." Key Engineering Materials 353-358 (September 2007): 2720–23. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2720.

Full text

Abstract:

Based on the von Kármán classical nonlinear plate theory, nonlinear axisymmetric vibrations of a clamped thin circular plate subjected to transverse harmonic load are investigated. Effects of static deformation on the vibration responses are considered. Harmonic motion is assumed. The time variable is eliminated and the partial differential equations are converted into a system of nonlinear ordinary differential equations by employing a Kantorovich time averaging method. The resulting nonlinear ordinary differential boundary-value problem is solved numerically by using shooting method. Effects of static-dynamic load on the transverse deflection, frequencies and amplitudes are examined in details. The resonance phenomenon is discussed emphatically.

APA, Harvard, Vancouver, ISO, and other styles

38

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 (January 1, 1994): 61–66. http://dx.doi.org/10.1115/1.2930397.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

39

Sun, Yuxin, Yan Jiang, and Jialing Yang. "Thermoelastic damping of the axisymmetric vibration of laminated trilayered circular plate resonators." Canadian Journal of Physics 92, no. 9 (September 2014): 1026–32. http://dx.doi.org/10.1139/cjp-2013-0374.

Full text

Abstract:

Thermoelastic damping is a critical loss mechanism in micromachined resonators used for sensing and communication applications. In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results. Then the effect of material selection and the volume fraction of the covering layers are numerically evaluated. Finally, the thermoelastic damping for different vibration modes is also evaluated.

APA, Harvard, Vancouver, ISO, and other styles

40

Mirtalaie, S. H., and M. A. Hajabasi. "Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 3 (September 10, 2010): 568–83. http://dx.doi.org/10.1243/09544062jmes2232.

Full text

Abstract:

In this article, the differential quadrature method (DQM) is used to study the free vibration of functionally graded (FG) thin annular sector plates. The material properties of the FG-plate are assumed to vary continuously through the thickness, according to the power-law distribution. The governing differential equations of motion are derived based on the classical plate theory and solved numerically using DQM. The natural frequencies of thin FG annular sector plates under various combinations of clamped, free, and simply supported boundary conditions are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate. In this case, the result shows very good agreement. For the FG-plates, the effects of boundary conditions, volume fraction exponent, and variation of Poisson's ratio on the free vibrational behaviour of the plate are studied.

APA, Harvard, Vancouver, ISO, and other styles

41

El-Sayad, Mohamed A., and Ahmed M. Farag. "Semi-Analytical Solution Based on Strip Method for Buckling and Vibration of Isotropic Plate." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/796274.

Full text

Abstract:

The present paper achieves a semianalytical solution for the buckling and vibration of isotropic rectangular plates. Two opposite edges of plate are simply supported and others are either free, simply supported, or clamped restrained against rotation. The general Levy type solution and strip technique are employed with transition matrix method to develop a semianalytical approach for analyzing the buckling and vibration of rectangular plates. The present analytical approach depends on reducing the strips number of the decomposed domain of plate without escaping the results accuracy. For this target, the transition matrix is expressed analytically as a series with sufficient truncation numbers. The effect of the uni-axial and bi-axial in-plane forces on the natural frequency parameters and mode shapes of restrained plate is studied. The critical buckling of rectangular plate under compressive in-plane forces is also examined. Analytical results of buckling loads and vibration frequencies are obtained for various types of boundary conditions. The influences of the aspect ratios, buckling forces, and coefficients of restraint on the buckling and vibration behavior of rectangular plates are investigated. The presented analytical results may serve as benchmark solutions for such plates. The convergence and efficiency of the present technique are demonstrated by several numerical examples compared with those available in the published literature. The results show fast convergence and stability in good agreement with compressions.

APA, Harvard, Vancouver, ISO, and other styles

42

Krishnappa, G., and J. M. McDougall. "Sound Intensity Distribution and Energy Flow in the Nearfield of a Clamped Circular Plate." Journal of Vibration and Acoustics 111, no. 4 (October 1, 1989): 465–71. http://dx.doi.org/10.1115/1.3269884.

Full text

Abstract:

Sound intensity distribution and energy flow in the nearfield of a clamped circular plate vibrating at its resonant frequencies were investigated. Theoretical calculation of the sound intensity vector was based on Rayleigh’s integral formula and the finite difference approximation of pressures to determine the particle velocity of sound in the fluid medium. The theoretically determined nearfield sound intensity distributions agreed well with the experimental measurements carried out using the two microphone method. Energy lines plotted on radial planes using the method suggested by Waterhouse et al. [3] for the axisymmetric modes of vibration showed the presence of vortex lines close to the nodal lines. The recirculating energy zones appeared to increase with the number of nodal circles, with the farfield radiation predominantly emanating from the center and outer edges of the plate. The theoretical results also revealed the existence of recirculating energy zones for the nonaxisymmetric modes of vibration.

APA, Harvard, Vancouver, ISO, and other styles

43

Xing, Y. F., Z. K. Wang, and T. F. Xu. "Closed-form Analytical Solutions for Free Vibration of Rectangular Functionally Graded Thin Plates in Thermal Environment." International Journal of Applied Mechanics 10, no. 03 (April 2018): 1850025. http://dx.doi.org/10.1142/s1758825118500254.

Full text

Abstract:

Based on classical small deflection plate theory, the governing equation of functionally graded (FG) plates in thermal environment is derived by using Hamilton’s principle. Closed-form analytical solutions are obtained via separation-of-variable method for free vibration of rectangular FG thin plates with simply supported, clamped and guided edges, especially for the plates with two adjacent clamped edges in thermal environment. The normal modes and frequencies are in an elegant and explicit closed form. Comprehensive numerical comparison and results in dimensionless form validate the present method and reveal a few physical phenomena.

APA, Harvard, Vancouver, ISO, and other styles

44

Xiang, Song, Hong Shi, Ke-ming Wang, Yan-ting Ai, and Yun-dong Sha. "Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates." European Journal of Mechanics - A/Solids 29, no. 5 (September 2010): 844–50. http://dx.doi.org/10.1016/j.euromechsol.2010.02.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Ayoub, E. F., and A. W. Leissa. "Free Vibration and Tension Buckling of Circular Plates With Diametral Point Forces." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 995–99. http://dx.doi.org/10.1115/1.2897673.

Full text

Abstract:

This paper presents the first known results for the free vibrations of a circular plate subjected to a pair of static, concentrated forces acting on the boundary at opposite ends of a diameter. The closed-form exact solution of the plane elasticity problem is used to provide the in-plane stress distribution for the vibration problem. A proper procedure using the Ritz method is developed for solving the latter problem for clamped, simply supported, or free boundary conditions. Numerical results are given for the vibration frequencies of a simply supported circular plate, which separate into four symmetry classes of mode shapes. Compressive buckling loads for each symmetry class are determined as a special case as the frequencies decrease to zero with increasing compressive force. Tracking the frequency versus loading data with increasing tensile forces shows that buckling due to tensile force can also occur, and the critical value of the force is found.

APA, Harvard, Vancouver, ISO, and other styles

46

MARETIC, R., V. GLAVARDANOV, and V. MILOSEVIC-MITIC. "VIBRATION AND STABILITY OF A HEAVY AND HEATED VERTICAL CIRCULAR PLATE." International Journal of Structural Stability and Dynamics 10, no. 05 (December 2010): 1111–21. http://dx.doi.org/10.1142/s0219455410003920.

Full text

Abstract:

This paper is concerned with the vibration and stability of a standing, heavy, and circular plate when heated. This investigation also deals with the plate being exposed to inertial forces due to uniform acceleration. The plate edge is clamped. Natural frequencies of transverse vibrations depending on the plate weight and temperature were determined using the Galerkin's method. Mode shapes are given for some frequencies including the influence of weight parameter on changes in mode shapes. It is shown that frequencies split for the asymmetric mode shapes, so that there are two different frequencies in those cases. Critical weight parameter values where plate stability ceases were determined. Critical values of the weight parameter depending on Poisson's ratio are also presented herein.

APA, Harvard, Vancouver, ISO, and other styles

47

Hanane, Moulay Abdelali, Khalid El Bikri, and Benamar Rhali. "Geometrically Non-Linear Free Vibration of Fully Clamped FGM Skew Plates Using Homogenization Technique." Advanced Materials Research 1105 (May 2015): 370–80. http://dx.doi.org/10.4028/www.scientific.net/amr.1105.370.

Full text

Abstract:

The present work concerns the geometrically non-linear free vibration of fully clamped functionally graded skew plates (FGSP). The theoretical model based on Hamilton’s principle and spectral analysis is used. A homogenization technique has been developed to reduce the FGSP problem under consideration to that of an isotropic homogeneous skew plate. The material properties of the skew plate examined herein are assumed to be graded in the thickness direction of the plate according to the power-law distribution in terms of volume fractions of the constituents. Results are given for the linear and non-linear fundamental frequency considering different parameters. The non-linear mode shapes exhibit a maximum value in the bending stress at the centre of the plate. It is found also that the non-linear frequencies increase with increasing the amplitude of vibration and increasing the skew angle, which corresponds to the hardening type effect. A good agreement is found with published results.

APA, Harvard, Vancouver, ISO, and other styles

48

Santos, Emily V., and Murray S. Korman. "Nonlinear vibration experiment: Clamped circular elastic plate with granular material loading." Journal of the Acoustical Society of America 139, no. 4 (April 2016): 2094. http://dx.doi.org/10.1121/1.4950214.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Qi, Hongyuan, and Yiduo Guan. "Fundamental frequency and testing mode of complicated elastic clamped-plate vibration." Frontiers of Mechanical Engineering in China 3, no. 4 (October 1, 2008): 360–64. http://dx.doi.org/10.1007/s11465-008-0084-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Ingber, M. S., A. L. Pate, and J. M. Salazar. "Vibration of a clamped plate with concentrated mass and spring attachments." Journal of Sound and Vibration 153, no. 1 (February 1992): 143–66. http://dx.doi.org/10.1016/0022-460x(92)90633-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Clamped plate vibration'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles