Discrete singular convolution for the prediction of high frequency vibration of plates

Theoretical analysis of high frequency vibrations is indispensable in a variety of engineering designs. Much effort has been made on this subject in the past few decades. However, there is no single technique which can be applied with confidence to various engineering structures for high frequency predictions at present. This paper introduces a novel computational approach, the discrete singular convolution (DSC) algorithm, for high frequency vibration analysis of plate structures. Square plates with six distinct boundary conditions are considered. To validate the proposed method, a completely independent approach, the Levy method, is employed to provide exact solutions for a comparison. The proposed method is also validated by convergence studies. We demonstrate the ability of the DSC algorithm for high frequency vibration analysis by providing extremely accurate frequency parameters for plates vibrating in the first 5000 modes.

[1]  G. Wei.  Discrete singular convolution for beam analysis , 2001 .

[2]  Mark J. Ablowitz,et al.  Regular ArticleOn the Numerical Solution of the Sine–Gordon Equation: I. Integrable Discretizations and Homoclinic Manifolds , 1996 .

[3]  Shuguang Guan,et al.  Fourier-Bessel analysis of patterns in a circular domain , 2001 .

[4]  N. S. Bardell,et al.  Free vibration analysis of a flat plate using the hierarchical finite element method , 1991 .

[5]  Richard H. Lyon.  Statistical energy analysis of dynamical systems : theory and applications , 2003 .

[6]  Haym Benaroya,et al.  Periodic and near-periodic structures , 1995 .

[7]  R. Langley,et al.  Prediction of high frequency vibration levels in built-up structures by using wave intensity analysis , 1995 .

[8]  Robin S. Langley,et al.  A review of current analysis capabilities applicable to the high frequency vibration prediction of aerospace structures , 1998, The Aeronautical Journal (1968).

[9]  Yang Xiang,et al.  Plate vibration under irregular internal supports , 2002 .

[10]  Guo-Wei Wei,et al.  Solving quantum eigenvalue problems by discrete singular convolution , 2000 .

[11]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[12]  T. M. Wang,et al.  Vibrations of frame structures according to the Timoshenko theory , 1971 .

[13]  Liwen Qian,et al.  A Note on Regularized Shannon's Sampling Formulae , 2000 .

[14]  Yang Xiang,et al.  Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm , 2002 .

[15]  Mark J. Ablowitz,et al.  On the Numerical Solution of the Sine-Gordon Equation , 1996 .

[16]  Jean Nicolas,et al.  A HIERARCHICAL FUNCTIONS SET FOR PREDICTING VERY HIGH ORDER PLATE BENDING MODES WITH ANY BOUNDARY CONDITIONS , 1997 .

[17]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[18]  Guo-Wei Wei,et al.  A new algorithm for solving some mechanical problems , 2001 .

[19]  J. R. Banerjee,et al.  An exact dynamic stiffness matrix for coupled extensional-torsional vibration of structural members , 1994 .

[20]  G. W. Wei,et al.  Generalized Perona-Malik equation for image restoration , 1999, IEEE Signal Processing Letters.

[21]  Guo-Wei Wei.  Wavelets generated by using discrete singular convolution kernels , 2000 .

[22]  L. Vázquez,et al.  Numerical solution of the sine-Gordon equation , 1986 .

[23]  D. M. Mead,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES: RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON, 1964–1995 , 1996 .

[24]  Andy J. Keane,et al.  Statistical energy analysis of strongly coupled systems , 1987 .

[25]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[26]  Guo-Wei Wei,et al.  Discrete Singular Convolution-Finite Subdomain Method for the Solution of Incompressible Viscous Flows , 2002 .

[27]  Guo-Wei Wei,et al.  VIBRATION ANALYSIS BY DISCRETE SINGULAR CONVOLUTION , 2001 .

[28]  G. Wei,et al.  A unified approach for the solution of the Fokker-Planck equation , 2000, physics/0004074.

[29]  Guo-Wei Wei,et al.  Discrete singular convolution for the sine-Gordon equation , 2000 .

[30]  Yang Xiang,et al.  Exact buckling solutions for composite laminates: proper free edge conditions under in-plane loadings , 1996 .

[31]  Hiroyuki Tamura,et al.  Theory and Algorithm , 1979 .

[32]  Guo-Wei Wei,et al.  Discrete singular convolution for the solution of the Fokker–Planck equation , 1999 .