A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports

Ye, Tiangui; Jin, Guoyong; Su, Zhu; Chen, Yuehua

doi:10.1016/j.ijmecsci.2014.01.001

Cited by 59 publications

(28 citation statements)

References 63 publications

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“…[4,5], we can easily get the total kinetic energy (T) and strain energy (V ) and . For the case considered, the total energy , due to multi-points supports, and the strain energy U , due to the Pasternak foundations, are given by:…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

Zhang¹,

Shi

Wang³

2016

Kms

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An improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with general elastic supports and point supports resting on an elastic foundation. The approach is based on the first order shear deformation theory and foundation effect using two-parameter Pasternak foundation model. The displacement and rotation functions are generally sought, regardless of boundary conditions, as Fourier series and supplementary functions. All the series expansion coefficients are determined using the Rayleigh-Ritz technique. The excellent accuracy of the current results is validated by comparing them with existing results.

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Section: Methodsmentioning

confidence: 99%

“…[5,6]. Finally, we arrive at the following matrix equation, from which the natural frequencies can be obtained by solving a standard matrix Eigen problem:…”

Section: Methodsmentioning

confidence: 99%

Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

Zhang¹,

Shi

Wang³

2016

Kms

View full text Add to dashboard Cite

show abstract

“…More information about the artificial spring boundary technique can be seen at Refs. [55,56]. Applying the artificial spring boundary technique, the deformation strain energy about the boundary springs (U sp ) can be given as: …”

Section: Energy Expressionsmentioning

confidence: 99%

Vibrations of composite laminated doubly-curved shells of revolution with elastic restraints including shear deformation, rotary inertia and initial curvature

Jin

Zhang

2015

Composite Structures

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“…In the practical application, the Pasternak model (also referred to as the two-parameter model) [24][25][26] is widely used to describe the mechanical behavior of the foundation, in which the wellknown Winkler model [27] is a special case. In addition, the boundary condition may not always be classical case in reality, and a variety of possible boundary conditions including classical boundary conditions, elastic boundary restraints, and the combinations of two or more conditions may be encountered [6][7][8][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Based on the open published paper, we can know that merely Zhou et al [48,49] extended the Chebyshev-Ritz method to study the free vibration characteristics of rectangular thick plates and thick circular plates resting on elastic foundations, respectively.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

Liu

Jing

et al. 2017

Shock and Vibration

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This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh-Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

show abstract

A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports

Cited by 59 publications

References 63 publications

Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

Vibrations of composite laminated doubly-curved shells of revolution with elastic restraints including shear deformation, rotary inertia and initial curvature

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

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