Wavelet based spectral finite element for analysis of coupled wave propagation in higher order composite beams

Composite Structures

Volumn 73, Issue 3, 2006, Pages 263-277

  Mitra, Mira ^a   Gopalakrishnan, S ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Composite beam; Finite element; Spectral finite element; Wave propagation; Wavelets

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; FREQUENCY DOMAIN ANALYSIS; LOADS (FORCES); ORDINARY DIFFERENTIAL EQUATIONS; SPECTRUM ANALYSIS; TIME DOMAIN ANALYSIS; WAVELET TRANSFORMS;

DAUBECHIES WAVELET BASIS; HIGHER ORDER EFFECTS; PULSE EXCITATION; TRANSVERSE DISPLACEMENTS; WAVELET BASED SPECTRAL FINITE ELEMENT;

COMPOSITE BEAMS AND GIRDERS;

COMPOSITE; FINITE ELEMENT ANALYSIS; STRUCTURAL ANALYSIS;

EID: 33644608154     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2005.01.038     Document Type: Article

References (35)

1. K. Amaratunga J.R. Williams S. Qian J. Weiss Wavelet-Galerkin solutions for one-dimensional partial differential equations Int. J. Numer. Meth. Eng. 37 1994 2703-2716
2. K. Amaratunga J.R. Williams S. Qian J. Weiss Wavelet based Green's function approach to 2D PDEs Eng. Comput. 10 4 1993 349-367
3. S. Qian J. Weiss Wavelets and the numerical solution of partial differential equations J. Comput. Phys. 106 1 1993 155-175
4. Glowinski R, Lawton W, Ravachol M, Tanenbaum, E. Wavelet solution of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension. In: Proceedings of the 9th International Conference on Numerical Methods in Applied Sciences and Engineering, SIAM, Philadelphia, 1990.
5. P. Joly Y. Maday V. Perrier Towards a method for solving partial differential equations by using wavelet packet bases Comput. Meth. Appl. Mech. Eng. 116 2 1994 193-202
6. W. Dahmen Wavelet methods for PDEs some recent developments J. Comput. Appl. Math. 128 1-2 2001 133-185
7. I. Daubechis Orthonormal bases of compactly supported wavelets Comm. Pure Appl. Math. 41 1988 906-966
8. I. Daubechis Ten lectures on wavelets. CBMS-NSF Series in Applied Mathematics 1992 SIAM Philadelphia
9. J.F. Doyle Wave propagation in structures 1999 Springer New York
10. J.F. Doyle A spectrally formulated finite element for longitudinal wave propagation Int. J. Anal. Exp. Modal Anal. 3 1988 1-5
11. J.F. Doyle T.N. Farris A spectrally formulated finite element for flexural wave propagation in beams Int. J. Anal. Exp. Modal Anal. 5 1990 13-23
12. J.F. Doyle T.N. Farris A spectrally formulated finite element for wave propagation in 3-d frame structures Int. J. Anal. Exp. Modal Anal. 22 1990 223-237
13. S. Gopalakrishnan M. Martin J.F. Doyle A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beam J. Sound Vib. 158 1992 11-24
14. M. Martin S. Gopalakrishnan J.F. Doyle Wave propagation in multiply connected deep waveguides J. Sound Vib. 174 4 1994 521-538
15. J.O.A. Robertsson J.O. Blanch W.W. Symes C.S. Burrus Galerkin-wavelet modeling of wave propagation: Optimal finite-difference stencil design Math. Comput. Modell. 19 1994 31-38
16. Joly P, Komatitsch D, Vilotte JP. The solution of the wave equation by wavelet basis approximation. In: Proceedings of the 1st Conference on Numerical Mathematics and Advanced Applications, Paris, 1995.
17. T.K. Hong B.L.N. Kennett On a wavelet based method for the numerical simulation of wave propagation J. Comput. Phys. 183 2002 577-622
18. Mitra M, Gopalakrishnan S. Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides. Int J Solids Struct, accepted for publication.
19. J.R. Williams K. Amaratunga A discrete wavelet transform without edge effects using wavelet extrapolation J. Fourier Anal. Appl. 3 4 1997 435-449
20. K. Amaratunga J.R. Williams Wavelet-Galerkin solution of boundary value problems Arch. Comput. Meth. Eng. 4 3 1997 243-285
21. Amaratunga K, Williams JR. Time integration using wavelets. In: Proceedings of SPIE, Wavelet Application for Dual Use 2491, Orlando, FL, 1995, pp. 894-902.
22. Mitra M, Gopalakrishnan S. Extraction of wave characteristics from wavelet based spectral finite element formulation. Mechanical Systems and Signal Processing, in press.
23. L. Zhang S.T. Quek Q. Wang A note on wavelet-based method for damage detection J. Appl. Mech. 68 2001 812-814
24. S. Yuan W. Lei L. Shi Active monitoring for on-line damage detection in composite structures J. Vib. Acoust. 125 2003 178-186
25. H. Sohn G. Park J.R. Wait N.P. Limback C.R. Farrar Wavelet-based active sensing for delamination detection in composite structures Smart Mater. Struct. 13 2004 153-160
26. H. Jeong Y.S. Jang Wavelet analysis of plate wave propagation in composite laminates Compos. Struct. 49 2000 443-450
27. Mindlin RD, Herrmann G. A one dimensional theory of compressional waves in an elastic rod. In: Proceedings of First U.S. National Congress of Applied Mechanics, 1950, pp. 187-91.
28. D.R. Mahapatra S. Gopalakrishnan A spectral finite element model for analysis of axial flexural shear coupled wave propagation in laminated composite beams Compos. Struct. 59 1 2003 67-88
29. D.R. Mahapatra S. Gopalakrishnan T.S. Shankar Spectral-element-based solution for wave propagation analysis of multiply connected unsymmetric laminated composite beams J. Sound Vib. 237 5 2000 819-836
30. A. Chakraborty S. Gopalakrishnan A spectrally formulated finite element for wave propagation analysis in functionally graded beams Int. J. Solid Struct. 40 10 2003 2421-2448
31. G. Beylkin On the representation of operators in bases of compactly supported wavelets SIAM J. Numer. Anal. 6 6 1992 1716-1740
32. S. Qian J. Weiss Wavelets and the numerical solution of boundary value problems Appl. Math. Lett. 6 1 1993 47-52
33. P.J. Davis Interpolation and approximation 1963 Blaisdell New York
34. J.R. Williams K. Amaratunga Introduction to wavelets in engineering Int. J. Numer. Meth. Eng. 37 1994 2365-2388
35. A. Chakraborty S. Gopalakrishnan A higher order spectral element for wave propagation analysis in functionally graded materials Acta Mechanica 172 1-2 2005 17-43