Wavelet spectral finite element for wave propagation in shear deformable laminated composite plates

This paper presents a new 2-D wavelet spectral finite element (WSFE) model for studying wave propagation in thin to moderately thick anisotropic composite laminates. The WSFE formulation is based on the first order shear deformation theory (FSDT) which yields accurate results for wave motion at high frequencies. The wave equations are reduced to ordinary differential equations (ODEs) using Daubechies compactly supported, orthonormal, scaling functions for approximations in time and one spatial dimension. The ODEs are decoupled through an eigenvalue analysis and then solved exactly to obtain the shape functions used in element formulation. The developed spectral element captures the exact inertial distribution, hence a single element is sufficient to model a laminate of any dimension in the absence of discontinuities. The 2-D WSFE model is highly efficient computationally and provides a direct relationship between system input and output in the frequency domain. Results for axial and transverse wave propagations in laminated composite plates of various configurations show excellent agreement with finite element simulations using Abaqus®.

[1]  Mira Mitra,et al.  Extraction of wave characteristics from wavelet-based spectral finite element formulation , 2006 .

[2]  Mira Mitra,et al.  Wavelet based 2-D spectral finite element formulation for wave propagation analysis in isotropic plates , 2006 .

[3]  William H. Prosser,et al.  Plate Mode Velocities in Graphite/Epoxy Plates , 1996 .

[4]  Constantinos Soutis,et al.  Structural health monitoring techniques for aircraft composite structures , 2010 .

[5]  Carlos E. S. Cesnik,et al.  Review of guided-wave structural health monitoring , 2007 .

[6]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[7]  Mira Mitra,et al.  Wave Propagation Analysis in Anisotropic Plate Using Wavelet Spectral Element Approach , 2008 .

[8]  Ozden O. Ochoa,et al.  Finite Element Analysis of Composite Laminates , 1992 .

[9]  Massimo Ruzzene,et al.  Spectral Finite Element Method , 2011 .

[10]  Arvind H. Shah,et al.  Elastic Waves in Composite Media and Structures: With Applications to Ultrasonic Nondestructive Evaluation , 2008 .

[11]  Chun H. Wang,et al.  Mindlin plate theory for damage detection: Source solutions , 2004 .

[12]  Srinivasan Gopalakrishnan,et al.  A spectrally formulated plate element for wave propagation analysis in anisotropic material , 2005 .

[13]  S. Gopalakrishnan,et al.  Wavelet based spectral finite element for analysis of coupled wave propagation in higher order composite beams , 2006 .

[14]  Kevin Amaratunga,et al.  A Discrete Wavelet Transform without edge effects using wavelet extrapolation , 1997 .

[15]  Adnan H. Nayfeh,et al.  Wave propagation in layered anisotropic media : with applications to composites , 1995 .

[16]  Mira Mitra,et al.  Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides , 2005 .

[17]  D. Chimenti.  Guided Waves in Plates and Their Use in Materials Characterization , 1997 .

[18]  Lin Ye,et al.  Guided Lamb waves for identification of damage in composite structures: A review , 2006 .

[19]  James F. Doyle,et al.  Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms , 1997 .

[20]  G. Beylkin.  On the representation of operators in bases of compactly supported wavelets , 1992 .

[21]  J. Rose.  Ultrasonic Waves in Solid Media , 1999 .

[22]  R. C. Stiffler,et al.  Low Frequency Flexural Wave Propagation in Laminated Composite Plates , 1988 .

[23]  Fu-Kuo Chang,et al.  Encyclopedia of structural health monitoring , 2009 .