DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges (original) (raw)
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Mechanics of Advanced Materials and Structures, 2012
A simple formulation for studying the free vibration of shear-deformable antisymmetric angle-ply laminated rectangular plates having translational as well as rotational edge constraints is presented. The aim is to fill the void in the available literature. The spatial discretization of the resulting mathematical model in five field variables is carried out using the two-dimensional Differential Quadrature Method. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes. The results are compared with those from past investigations available only for simpler problems. Effects of material, geometrical, and support parameters are studied.
The application of FEM is shown for free vibration analysis of moderately thick laminated composite plates with edges elastically restrained against translation and rotation. The governing equations employed are based on the first order shear deformation theory including the effects of rotary inertia. Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Angle-ply and cross-ply laminates with different thickness-to-length ratios are examined. Comparisons are made with results for thin as well as moderately thick laminated plates.
Shock and Vibration, 1995
In the present work, laminates having two opposite edges simply supported are considered. The boundary conditions at the other two opposite edges may be general, and between these two edges, the thickness of the plate may be nonuniform. The theory used for the vibration analysis of such laminates includes shear deformation and rotatory inertia. The solution approach of the problem is semianalytical. By using the trigonometric functions describing the mode shapes between the simply supported edges, the governing plate equations are reduced to ordinary differential equations. The solution of the reduced equations is then sought by the differential quadrature method. The results reported in this article serve two objectives of the present investigations. One, it is demonstrated that the proposed semianalytical quadrature method offers a numerically accurate and computationally efficient technique for the title problem. Two, the relative effects of shear deformation and rotatory inertia...
International Journal of Mechanical Sciences, 2011
This study presents a simple formulation for studying the free vibration of shear-deformable antisymmetric cross-ply laminated rectangular plates having translational as well as rotational edge constraints. The aim is to fill the void in the available literature with respect to the free vibration results of antisymmetric cross-ply laminated rectangular plates. The spatial discretization of the resulting mathematical model in five field variables is carried out using the two-dimensional Differential Quadrature Method (DQM). Several combinations of translational and rotational elastic edge constraints are considered. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available only for simpler problems. Effects of stiffness parameters, geometrical features, moduli ratio and lamination schemes on the natural frequencies are studied.
Vibration Analysis of Thick Arbitrarily Laminated Plates of Various Shapes and Edge Conditions
Free vibration analysis of arbitrarily laminated plates of quad, penta and hexagonal shapes, which have combinations of clamped, simply supported and free edge conditions is performed. The finite element formulation is based on first and higher order shear deformation theories to study the free vibration response of thick laminated composite plates. A finite element code is developed incorporating shear deformation theories using an 8-noded serendipity element. The effect of plate shape, arbitrary lamination and different edge conditions on natural frequencies and mode shapes are investigated. A systematic study is carried out to determine the influence of material orthotropy and aspect ratio on free vibration response. For various cases, the comparisons of results from present study showed good agreement with those published in the literature.
Free vibration analysis of composite plates using indirect quadrature technique
International Journal for Computational Methods in Engineering Science and Mechanics, 2019
This work concerns with free vibration analysis of composite plate materials. Based on a transvers shear theory, the governing equations of the problem are derived. An indirect technique of moving least-square differential quadrature method is developed and employed to reduce the problem to that of eigen-value one. Natural frequencies and mode shape functions of the composite are obtained. Validity of the developed technique is examined for regular and irregular plates with different boundary conditions. Accuracy and efficiency of the obtained results are achieved by comparing them with the previous exact and numerical ones. Further, a parametric study is introduced to investigate the effects of elastic and geometric properties on values of vibration field quantities. KEYWORDS Vibration; transverse shear theory; composite plate; regular and irregular domains; differential quadrature 2. Formulation of the problem Consider a non-homogeneous composite consisting of an isotropic plate bonded to another one made of a functionally graded material (FGM). The elastic characteristics of the composite vary such that:
European Journal of Mechanics - A/Solids, 2012
In this study, free vibration analysis of moderately thick symmetrically laminated general trapezoidal plates with various combinations of boundary conditions is investigated. The governing partial differential equations and boundary conditions for trapezoidal plate are obtained using first order shear deformation theory (FSDT) together with proper transformation from Cartesian system into trapezoidal coordinates. Generalized differential quadrature (GDQ) method is then employed to obtain solutions for the governing equations. Results of the GDQ method are compared and validated with available results in the literature which show accuracy and fast rate of convergence of the method. Effect of various parameters such as geometry, thickness, boundary condition and lay-up configuration on the natural frequency of trapezoidal and skew plates is investigated through several examples. It is also shown that the method can be used for analysis of triangular plates as special case of trapezoidal geometry with the same performance and convergence.
Computers & Structures, 2016
A method is presented to study the free vibrations of rectangular laminated composite plates with general layups and arbitrary boundary conditions. Based on the first-order shear deformation theory, the governing differential equations and boundary conditions are deduced via Hamilton's principle. Generalised displacements are expanded as series with Legendre polynomials as a base functions. A generalised eigenvalue problem is obtained by following a variational approach, where energy functional is extremised and boundary conditions are introduced by means of Lagrange multipliers. In order to overcome some difficulties in obtaining the natural frequencies and corresponding mode shapes, a new numerical strategy is proposed.
International Journal of Mechanical Sciences, 2014
This study presents, for the first time, free vibration results of laminated sector plates having elastic edges. Each layer is cylindrically orthotropic. A differential quadrature method (DQM) based formulation is used for studying the problem of shear-deformable laminated sector plates having translational as well as rotational edge constraints. By varying the edge stiffnesses, several combinations of simply supported and clamped edge conditions are simulated. The results are further validated by comparison with the results of laminated square plates (with elastic edges) and of laminated sector plates (without elastic edges) available in the literature.