Free vibration analysis of moderately thick antisymmetric angle-ply laminated rectangular plates with elastic edge constraints (original) (raw)
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Composite Structures, 2006
The application of differential quadrature method will be shown for free vibration analysis of moderately thick 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. Different combinations of constraints at edges are tested, which includes plates with at least a corner without a rigid support. Angle-ply and cross-ply laminates with different aspect ratios, thickness-to-length ratios are examined. Comparisons are made with results for thin as well as moderately thick angle-ply and cross-ply laminated plates. Highly accurate solutions can be achieved with only a few grid points.
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.
International Journal of Mechanical Sciences, 2011
Laminated composite plates are being used in structural elements needed in various technologycritical areas like aeronautics, space, automobile etc., primarily due to their low weight to strength ratio. During the past few decades, several researchers have been presenting solutions to bending, buckling and vibration problems of laminated plates. These many efforts have been necessitated by complexities arising due to various reasons like geometry, boundary conditions and material properties. Boundary conditions often lead to some difficult problem situations. Most of the research papers, including the most recent ones ([9] -[17]), present solutions for only classical boundary conditions. These classical boundary conditions have, corresponding to every degree of freedom, either the corresponding force (natural boundary conditions) or the displacement (essential boundary condition) as a prescribed quantity [37]. The more challenging and realistic boundary condition is the one which involves some suitable relationship between a displacement component and the corresponding force. These more realistic edge conditions are also being investigated by several researchers ([18] -[29]) with the help of a mathematical model known in literature as 'elastic edges'. The first known results of free vibration analysis of symmetrically laminated cross-ply rectangular plates with edges having uniform elastic restraints translational as well as rotational were presented by Liew et al. [18]. Shu and Wang [19] applied generalized differential quadrature method for the vibration analysis of thin isotropic plates with mixed and nonuniform boundary conditions. Zhou [20] applied the Rayleigh-Ritz method along with static Timoshenko beam functions for obtaining the natural frequencies of isotropic Mindlin rectangular plates. Friswell & Wang [21]
Composite Structures, 2008
Analytical formulations and solutions to the natural frequency analysis of simply supported antisymmetric angle-ply composite and sandwich plates hitherto not reported in the literature based on a higher order refined computational model with 12 degrees of freedom already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane displacements with respect to the thickness coordinate thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. In addition, another higher order computational model with five degrees of freedom already available in the literature is also considered for comparison. The equations of motion are obtained using Hamilton's principle. Solutions are obtained in closed-form using Navier's technique by solving the eigenvalue equation. Plates with varying slenderness ratios, number of layers, degrees of anisotropy, edge ratios and thickness of core to thickness of face sheet ratios are considered for analysis. Numerical results with real properties using above two computational models are presented and compared for the free vibration analysis of multilayer antisymmetric angle-ply composite and sandwich plates, which will serve as a benchmark for future investigations.
Computer Methods in Applied Mechanics and Engineering, 1997
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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...
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.
Vibration of angle-ply symmetric laminated composite plates with edges elastically restrained
Composite Structures, 2007
This paper presents semi-analytical solutions to determine the natural frequencies and the mode shapes of angle-ply laminated plates with edges elastically restrained. The finite strip transition matrix technique is extended to apply to angle-ply laminated plates with edges elastically restrained against rotation and translation. The effect of the edge conditions on the natural frequencies and mode shapes are presented. The convergence and comparison of the results with those available in the literature indicate the accuracy and the validity of the proposed technique. The effects of the elastic restraint parameters on the mode shapes are illustrated in graphic forms.
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.
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.