Generalised Differential Quadrature Method in the Study of Free Vibration Analysis of Monoclinic Rectangular Plates (original) (raw)
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Vibration of non-uniform thick plates on elastic foundation by differential quadrature method
Engineering Structures, 2004
This paper presents a differential quadrature (DQ) solution for free vibration analysis of thick plates of continuously varying thickness on two-parameter elastic foundations. The formulations are based on the first-order shear deformation theory taking into account the effects of rotary inertia. The thickness of the plate may vary in one or two directions. The thickness variation might be assumed linear or non-linear. Different types of boundary conditions, including free edges and corners, loaded edges with in-plane forces are formulated. The accuracy, convergence and versatility of the DQ procedure for the type of plate problems, with complicated governing differential equations and boundary conditions are examined and verified. #
Application of a new differential quadrature methodology for free vibration analysis of plates
International Journal for Numerical Methods in Engineering, 2003
A new methodology is introduced in the differential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a different manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of difficulty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and/or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods. Copyright © 2002 John Wiley & Sons, Ltd.
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.
The free vibration analysis of point supported rectangular plates using quadrature element method
Journal of Theoretical and Applied Mechanics, 2017
In this study, the hybrid approach of the Quadrature Element Method (QEM) has been employed to generate solutions for point supported isotropic plates. The Hybrid QEM technique consists of a collocation method with the Galerkin finite element technique to combine the high accurate and rapid converging of Differential Quadrature Method (DQM) for efficient solution of differential equations. To present the validity of the solutions, the results have been compared with other known solutions for point supported rectangular plates. In addition, different solutions are carried out for different type boundary conditions, different locations and number of point supports. Results for the first vibration modes of plates are also tested using a commercial finite element code, and it is shown that they are in good agreement with literature.
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This paper presents a differential quadrature solution for analysis of transverse vibrations of non-homogeneous rectangular orthotropic plates of linearly varying thickness resting on Winkler foundation. Following Lévy approach i.e. two parallel edges are simply supported, the governing equation of motion has been solved for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. Numerical results for first three natural frequencies for various values of parameters are presented in tables and graphs. The accuracy and convergence results are examined and verified.
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A differential quadrature method is presented for computation of the fundamental frequency of a thin single-layer specially orthotropic and anisotropic rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomial functions for the differential operators. By doing this, the uncoupled and coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations. The results for the eigenvalue (or fundamental frequency) for all the cases analyzed are compared with solutions obtained by another numerical method. Effects of level of discretization, boundary conditions, aspect ratio and taper ratio on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use much less computer time.
International Journal Of Engineering & Applied Sciences
Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of nonhomogeneous rectangular orthotropic plates of linearly varying thickness resting on two-parameter foundation (Pasternak). The analysis is based on classical plate theory. Numerical results are presented for various values of plate parameters for different boundary conditions. Convergence studies have been made to ensure accuracy of the results. A comparison of our results with those available in the literature shows the versatility and accuracy of DQM.
The differential quadrature method for irregular domains and application to plate vibration
International Journal of Mechanical Sciences, 1996
By its very basis, the differential quadrature method may be applied to domains having boundaries oriented along the coordinate axes. In this paper, it is shown that quadrature rules may also be formulated for irregular domains using the natural-to-Cartesian geometric mapping technique. The application of the technique is demonstrated through the vibration analysis of thin isotropic plates of general quadrilateral and sectorial planforms.
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.