Spectral element modeling and analysis of the transverse vibration of a laminated composite plate

This paper presents a frequency-domain spectral element model for the symmetric laminated composite plates which have finite dimensions in two orthogonal directions, i.e., in the x- and y-directions. The spectral element model is developed by using two methods in combination: the splitting of original boundary conditions and the so-called super spectral element method in which both the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes (or degrees of freedom (DOFs)) only on four edges of a finite element, i.e., no nodes inside the finite element. Accordingly the total number of DOFs used in the dynamic analysis can be drastically decreased to lead to a significant decrease of the computation cost, when compared with the standard finite element method (FEM). The high accuracy of the present spectral element model is verified in due course by the comparison with the results by two solution methods: the exact theory available in the literature and the standard finite element model developed in this study.

[1]  U. Lee.  Spectral Element Method in Structural Dynamics , 2009 .

[2]  J. R. Banerjee,et al.  Dynamic stiffness elements and their applications for plates using first order shear deformation theory , 2011 .

[3]  S. Kevorkian,et al.  The dynamic stiffness matrix of two-dimensional elements: application to Kirchhoff's plate continuous elements , 2005 .

[4]  H. R. Mirdamadi,et al.  Frequency-dependent vibration analysis of symmetric cross-ply laminated plate of Levy-type by spectral element and finite strip procedures , 2013 .

[5]  Wieslaw Ostachowicz,et al.  Damage detection of structures using spectral finite element method , 2008 .

[6]  P. H. Kulla.  High precision finite elements , 1997 .

[7]  A. N. Berçin.  Analysis of orthotropic plate structures by the direct-dynamic stiffness method , 1995 .

[8]  James F. Doyle,et al.  Wave Propagation in Structures , 1989 .

[9]  D. J. Gorman,et al.  Free Vibration Analysis of Rectangular Plates , 1982 .

[10]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[11]  Marek Krawczuk,et al.  Wave propagation in plate structures for crack detection , 2004 .

[12]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[13]  Srinivasan Gopalakrishnan,et al.  A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate , 2006 .

[14]  Andrew Y. T. Leung,et al.  Dynamic stiffness analysis of laminated composite plates , 1996 .

[15]  Kajal K. Gupta,et al.  Finite Element Multidisciplinary Analysis, Second Edition , 2003 .

[16]  A. Cammarano,et al.  Waveguides of a Composite Plate by using the Spectral Finite Element Approach , 2009 .

[17]  Usik Lee,et al.  Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis , 2014 .

[18]  H. R. Mirdamadi,et al.  Free and transient vibration analysis of an un-symmetric cross-ply laminated plate by spectral finite elements , 2012 .

[19]  Svante Finnveden,et al.  A spectral super element for modelling of plate vibration. Part 1 : general theory , 2005 .

[20]  Svante Finnveden,et al.  Calculation of wave propagation in rib-stiffened plate structures , 1996 .

[21]  Usik Lee,et al.  Spectral-Element Method for Levy-Type Plates Subject to Dynamic Loads , 1999 .

[22]  A. Patera.  A spectral element method for fluid dynamics: Laminar flow in a channel expansion , 1984 .