Free vibration of moderately thick antisymmetric laminated annular sector 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.
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.
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.
36th Structures, Structural Dynamics and Materials Conference, 1995
In this paper, the analysis of the titled problem is based on classical thin plate theory and its numerical solution is carried out by a semi-analytical differential quadrature method. The thin rectangular plates considered herein arc simply supported on two opposites edges. Thc boundary conditions at the other two edges may be quite general and between these two edges, the plates may have varying thickness. However, the rcsults contained in this paper are for plates which are elastically restrained against rotation at the these edges and have linearly tapered thickness. On the basis of comparison with the available results in the published literature, it is bclicved that this solution method guarantees high numerical accuracy for the problem. Moreover, the computation times involved in the evaluation of free vibration characteristics are sufficiently small indicating that the solution method may possibly be further developed for the real time analysis and design of vibrating plate systems.
Axisymmetric free vibration of thick annular plates
International Journal of Mechanical Sciences, 1999
This paper presents a numerical analysis of the axisymmetric free vibration of moderately thick annular plates using the differential quadrature method (DQM). The plates are described by Mindlin's first-order shear-deformation theory. The first five axisymmetric natural frequencies are presented for uniform annular plates, of various radii and thickness ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of the plates. The accuracy of the method is established by comparing the DQM results with some exact and finite element numerical solutions and, therefore, the present DQM results could serve as a benchmark for future reference. The convergence characteristics of the method for thick plate eigenvalue problems are investigated and the versatility and simplicity of the method is established.
Transverse Vibration of Symmetrically Laminated Elastically Restrained Plates of Variable Thickness
The natural frequencies of symmetrically laminated plates of variable thickness are analyzed using the finite strip transition matrix technique. In this paper, the natural frequencies of such plates are determined for edges with elastic restrained against rotation, transition or both. A successive conjunction of the classical finite strip method and the transition matrix method is applied to develop a new modification of the finite strip method to reduce the complexity of the problem. The displacement function is expressed as the product of a basic trigonometric series function in the longitudinal direction and an unknown function that has to be determined in the other direction. Using the new transition matrix, after necessary simplification and the satisfaction of the boundary conditions, yields a set of simultaneous equations that leads to the characteristic matrix of vibration. Numerical results for different combinations of elastic rotational or transitional edges have been presented and compared with those available from other methods in the literature. Also, the effect of the tapered ratio and the aspect ratio on the natural frequencies of the plates is presented. The good agreement with other methods demonstrates the validity and the reliability of the proposed method.
Vibration Analysis of Annular Circular and Sector Plates with Non-Uniform Thickness
Far East Journal of Dynamical Systems, 2017
In this paper, generalized differential quadrature method (GDQM) is employed and vibration analysis of annular circular and sector plates with non-uniform thickness is investigated numerically. Natural frequencies and corresponding vibration modes are obtained for various boundary conditions. Accuracy and efficiency of the presented GDQM are tested against previous results for free vibration analysis of uniform ones and numerical results are proposed for free vibration analysis of annular circular plates with non-uniform thickness in three cases of linear variable thickness, parabolic variable thickness and exponential variable thickness and also for sector plates with linear variation in thickness. Meanwhile, effects of radii ratio, sector angle and variation of the thickness on the natural frequencies are investigated.
Stability and vibration of thick laminated composite sector plates
Journal of Sound and Vibration, 2005
This study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of shear deformable laminated sector plates made up of cylindrically orthotropic layers. The non-axisymmetric formulation in cylindrical coordinates is discretized in space domain in terms of twodimensional Chebyshev polynomials. Several combinations of simply supported, clamped and free edge conditions are considered. Convergence study has been carried out and the obtained results are compared with the results of laminated square plates and isotropic sector plates available in literature. Extensive results pertaining to critical buckling loads and natural frequencies are presented. Effects of boundary conditions, number of layers, moduli ratio, rotary and in-plane inertia, plate thickness, sector angle and annularity are studied.
Ocean Engineering, 2013
In this study maximum deflection and free vibration of quasi-isotropic thin rectangular plates that are clamped or simply supported from four edges were examined. The effects of changes in aspect ratio and orientation angle on the results of statical bending and free vibration problems according to the Classical Lamination Plate Theory were parametrically calculated by utilizing the Galerkin Method and the Least Squares Method among Weighted Residuals Methods. Obtained results were compared with the software package ANSYS that conducts analyses through Finite Elements Method (FEM). It is observed that the Galerkin Method yields reasonable results much more rapidly than FEM. It was determined that the effect of changes in orientation angles and aspect ratios of different combination of plates, which were constituted with the alternative arrangement of the lamination angles, on maximum deflection and fundamental natural frequency values is substantial. It was considered that the optimum plates that will properly satisfy different load conditions on the different parts of the structure can be determined with the use of the nondimensional tables prepared with the Galerkin Method in the preliminary design of composite hulls. It is proposed that savings from materials, labor, testing and time can be achieved by this means.
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.