An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports

Li, W.L.; Zhang, Xuefeng; Du, Jingtao; Liu, Zhigang

doi:10.1016/j.jsv.2008.09.035

Cited by 158 publications

(113 citation statements)

References 22 publications

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“…The deflection of the plates was calculated for several values of the foundation moduli and shown graphically as a function of time. More recently, study on an exact series solution for the transverse vibrations of rectangular plates with elastic boundary supports was carried out by [Li et al (2009)]. In this study, an analytical method was developed for the vibration analysis of rectangular plates with elastically restrained edges.…”

Section: Introductionmentioning

confidence: 99%

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Omolofe

Oni

2015

Lat. Am. j. solids struct.

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This study concerns the dynamic characteristics of a prestressed isotropic, rectangular plate continuously supported by an elastic foundation and carrying accelerating mass M. Closed form solutions of the governing fourth order partial differential equations with variable and singular coefficients are presented. For the twodimensional plate problem, the solution techniques is based on the double Fourier Finite Sine integral transformation, the expansion of the Dirac Delta function in series form, a modification of Struble's asymptotic method and the use of Fresnel sine and Fresnel cosine integrals. Numerical analyses in plotted curves are presented. The analyses reveal interesting results on the effect of structural parameters such as foundation moduli, rotatory inertia correction factor and prestressing forces on the dynamic behaviour of isotropic rectangular plate under the actions of concentrated masses moving at variable velocity. In particular it is found that the critical velocity of the travelling load which brings about the occurrence of a resonance state increases as the values of these structural parameters increase.

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Section: Introductionmentioning

confidence: 99%

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Omolofe

Oni

2015

Lat. Am. j. solids struct.

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“…Similar to the above acoustic analysis of enclosed sound space, the energy principle can also give the sufficiently accurate prediction of vibro-acoustic behaviour, when the admissible functions are constructed smooth enough. For the transverse vibration of a rectangular plate with general elastic boundary supports, its displacement function will be invariantly expanded into an improved Fourier series as [14].…”

Section: Vibro-acoustic Coupling Of Panel-cavity Systemmentioning

confidence: 99%

Acoustic Analysis of Enclosed Sound Space as well as Its Coupling with Flexible Boundary Structure

Du¹,

Liu²,

Liu³

2018

Computational and Experimental Studies of Acoustic Waves

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Combustion instability is often encountered in various power systems, a good understanding on the sound field in acoustic cavity as well as its coupling with boundary flexible structure will be of great help for the reliability design of such combustion system. An improved Fourier series method is presented for the acoustic/vibro-acoustic modelling of acoustic cavity as well as the panel-cavity coupling system. The structuralacoustic coupling system is described in a unified pattern using the energy principle. With the aim to construct the admissible functions sufficiently smooth for the enclosed sound space as well as the flexible boundary structure, the boundary-smoothed auxiliary functions are introduced to the standard multi-dimensional Fourier series. All the unknown coefficients and higher order variables are determined in conjunction with Rayleigh-Ritz procedure and differential operation term by term. Numerical examples are then presented to show the correctness and effectiveness of the current model. The model is verified through the comparison with those from analytic solution and other approaches. Based on the model established, the influence of boundary conditions on the acoustic and/or vibro-acoustic characteristics of the structural-acoustic coupling system is addressed and investigated.

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“…(4), the ability of convergence of series expansion in Eq. (4) was proved mathematically in reference [21]. For the series expansion is directly used in this paper, our attention will be focused on solving the unknown expansion coefficients by setting the assumed solution satisfy the governing equation and boundary conditions.…”

Section: Theorymentioning

confidence: 99%

“…In this paper, an approach based on the research by Li [20,21] is introduced to analyze the free vibration of elastically restrained beams carrying various types of attachments with arbitrary spatial distributions firstly. Some numerical examples are shown together with the solutions described in references to validate the methodology.…”

Section: Introductionmentioning

confidence: 99%

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

Xiao

Sheng

Liu

et al. 2013

Shock and Vibration

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Abstract. The flexible beams carrying attachments often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. This manuscript develops a proposed analytical method as a general tool for solving the free vibration of varying cross-section beams carrying various types of attachments with different distributions and arbitrary boundary conditions. In current practice, the natural frequencies of beam carrying lumped and uniform sprung mass and resting on Pasternak soil are calculated and compared with those in references to verify the methodology firstly. Then, the natural frequencies of beam carrying non-uniform spring-mass systems and stepped beam on Pasternak soil are calculated by the proposed method to study free vibration of beam carrying attachments with non-uniform cross section or distribution. Finally, some important conclusions are derived from results, which reveal that distribution density of spring-mass system at peaks of the mode shape makes dominate effects on the change of the natural frequencies at that mode and the natural frequencies of the stepped beam resting on elastic foundation are more sensitive to the increase of soil parameters.

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An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports

Cited by 158 publications

References 22 publications

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Acoustic Analysis of Enclosed Sound Space as well as Its Coupling with Flexible Boundary Structure

The Study on Free Vibration of Elastically Restrained Beams Carrying Various Types of Attachments with Arbitrary Spatial Distributions

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