A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Abstract

It is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Single Finite Fourier Sine Integral Transform Method for the Determination of Natural Frequencies of Flexural Vibration of Kirchhoff Plates

“…Table 1 reveals that the present results are comparable to previous results by Fetea [32] who used the Galerkin-Vlasov method to solve the same problem. The present results are also comparable with previous results obtained by Lim et al [30] who used the Finite Element Method (FEM), Eftekhari [27] who used Ritz-DQM, and Ghasochi-Bergh and Ravazi [28].…”

“…The ODE is solved using methods for solving differential equationstrial functions methodto obtain the solution in the transform space as Equation (23). The transform of the boundary conditions along the clamped edges (y = 0, and y = b) are used to generate the system of homogeneous equations given in matrix form as Equation (33 Table 1, which also presents solutions previously obtained by Chakraverty [1], Gorman [10], Ezeh et al [21], Lim et al [30], Eftekhari [27], Fetea [32], Lim and Liew [31], Leissa [2], Leissa and Qatu [6], Kalita and Dutta [15], and Njoku [25]. Table 1 reveals that the present results are comparable to previous results by Fetea [32] who used the Galerkin-Vlasov method to solve the same problem.…”

Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM)

“…Mahmoud et al [9] used GDQM for free vibration analysis of delaminated beam plates. Eftekhari conducted several studies of beams and plates on both linear [10][11][12] and nonlinear [13] dynamic problems, specifically for moving loads using the GDQM. He investigated many effects, such as sampling points and Dirac-delta function coefficients.…”