Plate vibration under irregular internal supports

Abstract

This paper studies the problem of plate vibration under complex and irregular internal support conditions. Such a problem has its widely spread industrial applications and has not been addressed in the literature yet, partially due to the numerical difficulties. A novel computational method, discrete singular convolution (DSC), is introduced for solving this problem. The DSC algorithm exhibits controllable accuracy for approximations and shows excellent flexibility in handling complex geometries, boundary conditions and internal support conditions. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. Case studies are considered to the combination of a few different boundary conditions and irregular internal supports. The latter are generated by using an image processing algorithm. Completely independent verifications are conducted by using the established pb-2 Ritz method, which is available for two relatively simpler support patterns. The morphology of the first few eigenmodes is found to be localized to largest support-free spatial regions. Ó

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

“…Wei and his co-workers first applied the DSC algorithm to solve mechanics problems [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Zhao et al [10,11] analyzed the high-frequency vibration of plates and plate vibration under irregular internal support using DSC algorithm. Wan et al [17,18] studied some fluid mechanics problem using DSC method.…”

“…In this study, we used the same procedure proposed by Wei et al [8,9,12] and Zhao et al [10,11]. In this paper, details of the implementation of boundary conditions in the DSC method are not given; interested readers may refer to the works of [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

The free vibration analysis of point supported rectangular plates using quadrature element method

“…Although there are no exact solutions for these problems, various numerical approaches have been utilized. For example, Cox and Boxer (1960) used a finite difference method, Damle and Feeser (1972) used the finite element method, Fan and Cheung (1984) used the spline finite strip method, Huang and Thambiratnam (2001a) used the finite strip method, Guiterrez and Laura (1995) used dthe ifferential quadrature method, Zhao et al (2002) used the discrete singular convolution method to solve the mentioned plate vibration problems. Because of its high accuracy, the Rayleight-Ritz method has been the most frequently used analytical method to appeal for vibration analysis of plates, as Narita and Hodgkinson (2005) did.…”

“…Zhou (2002) used a set of static tapered beam functions which were the solutions of a tapered beam under a Taylor series of static loads developed as admissible functions for vibration analysis of point-supported rectangular plates with variable thickness in one or two directions. Again, Zhao et al (2002) studied the problem of plate vibration under complex and irregular internal support conditions using the discrete singular convolution method. Kocatürk et al (2004) used Lagrange equations to examine the steady state response to a sinusoidally varying force applied at the centre of a viscoelastically point-supported orthotropic elastic plate of rectangular shape with considered locations of added masses.…”

Free Vibration Analysis of Rectangular Plates with Multiple Point Supports

“…The free vibration problems of the rectangular plates with point supports were also studied in references [4][5][6][7]. Recently, Zhao, Wei and Xiang [8] used discrete singular convolution method to solve plate In this paper, a discrete method [10][11][12][13] is extended for analyzing the free vibration of rectangular plates with multiple point supports. The fundamental differential equations of a plate with point supports involving Dirac's delta functions are established and satisfied exactly throughout the whole plate.…”