Free vibration analysis of laminated composite shallow shells with general elastic boundaries

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

doi:10.1016/j.compstruct.2013.07.005

Cited by 54 publications

(22 citation statements)

References 36 publications

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“…The vibration behaviors of a box-type built-up structure and energy transmission through the structure are solved analytically by Chen et al [2012]. A unified and exact solution method is developed in Ye et al [2013] for free vibration analysis of composite laminated shallow shells with general boundary conditions. Jin et al [2014] found a new three-dimensional exact solution for the free vibrations of arbitrarily thick FG rectangular plates using Rayleigh-Ritz procedure.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Functionally Graded Thin Rectangular Plates Resting on Winkler Elastic Foundation With General Boundary Conditions Using Rayleigh–ritz Method

Chakraverty

Pradhan

2014

Int. J. Appl. Mechanics

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In this paper, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of classical plate theory is investigated. Rayleigh-Ritz method is used to obtain the generalized eigenvalue problem. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of the FG plate are assumed to vary continuously in the thickness direction of the constituents according to power-law form. The objective is to study the effects of constituent volume fractions, aspect ratios and power-law indices on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. Comparison with the results from the existing literature are provided for validation in special cases. Three-dimensional mode shapes are presented for FG square plates having various boundary conditions at the edges for different power-law indices. The present investigation also involves the rectangular FG plate to lay on a uniform Winkler elastic foundation. New results for the eigenfrequencies associated with foundation parameters are also reported here with the validation in special cases after checking a convergence pattern.

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Section: Introductionmentioning

confidence: 99%

Free Vibration of Functionally Graded Thin Rectangular Plates Resting on Winkler Elastic Foundation With General Boundary Conditions Using Rayleigh–ritz Method

Chakraverty

Pradhan

2014

Int. J. Appl. Mechanics

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“…Herein, the length, width, and total thickness are represented by a, b, and h, respectively. The FGSSS considered here are characterized by the middle surface, which can be obtained by [45] = − (…”

Section: Methodsmentioning

confidence: 99%

Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Wang

Yao

et al. 2019

Mathematical Problems in Engineering

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In this investigation, an exact method based on the first-order shear deformation shallow shell theory (FSDSST) is performed for the free vibration of functionally graded sandwich shallow shells (FGSSS) on Winkler and Pasternak foundations with general boundary restraints. Vibration characteristics of the FGSSS have been obtained by the energy function represented in the orthogonal coordinates, in which the displacement and rotation components consisted of standard double Fourier cosine series and several closed-form supplementary functions are introduced to eliminate the potential jumps and boundary discontinuities. Then, the expansion coefficients are determined by using Rayleigh-Ritz method. The proposed method shows good accuracy and reliability by comprehensive investigation concerning free vibration of the FGSSS. Numerous new vibration results for FGSSS on Winkler and Pasternak foundations with various curvature types, geometrical parameters, and boundary restraints are provided, which may serve as benchmark solutions for future research. In addition, the effects of the inertia, shear deformation, and foundation coefficients on free vibration characteristic of FGSSS are illustrated.

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“…Some other contributors are given in Refs. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. The development of researches on this subject has been well documented in several monographs respectively by Reddy [22], Carrera et al [25], Qatu [44] and reviews [45][46][47][48].…”

Section: Introductionmentioning

confidence: 98%

Free vibration analysis of laminated composite shallow shells with general elastic boundaries

Cited by 54 publications

References 36 publications

Free Vibration of Functionally Graded Thin Rectangular Plates Resting on Winkler Elastic Foundation With General Boundary Conditions Using Rayleigh–ritz Method

Free Vibration of Functionally Graded Thin Rectangular Plates Resting on Winkler Elastic Foundation With General Boundary Conditions Using Rayleigh–ritz Method

Free Vibration of Functionally Graded Sandwich Shallow Shells on Winkler and Pasternak Foundations with General Boundary Restraints

Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions

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