Wave propagation in inhomogeneous layered media: Solution of forward and inverse problems

Acta Mechanica

Volumn 169, Issue 1-4, 2004, Pages 153-185

  Chakraborty, A ^a,b   Gopalakrishnan, S ^a,b  

^a Indian Institute of Sceince ^*

^b INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

FAST FOURIER TRANSFORMS; FINITE ELEMENT METHOD; FUNCTIONALLY GRADED MATERIALS; INVERSE PROBLEMS; LINEAR ALGEBRA; MATHEMATICAL MODELS; OPTIMIZATION; RESIDUAL STRESSES; STIFFNESS MATRIX; THERMAL CONDUCTIVITY; THERMAL STRESS; TIME DOMAIN ANALYSIS; TRANSFER FUNCTIONS;

MULTI-LAYERED STRUCTURES; PARTIAL WAVE TECHNIQUE (PWT); SPECTRAL LAYER ELEMENT (SLE); THERMO-MECHANICAL LOADING;

WAVE PROPAGATION;

EID: 3042593394     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-004-0080-7     Document Type: Article

References (71)

1. Suresh, S., Mortensen, A.: Fundamentals of functionally graded materials. London: IOM Communications 1998.
2. Kuhlemeyer, R. L., Lysmer, J.: Finite element accuracy for wave propagation problems. J. Soil Mech. Foundations Division, ASCE 99(SM5), 421-427 (1973).
3. Chatfield, C.: The analysis of time series. London: Chapman and Hall 1984.
4. Doyle, J. F.: A spectrally formulated finite element for longitudinal wave propagation. Int. J. Anal. Exp. Modal Analysis 3, 1-5 (1988).
5. Doyle, J. F., Farris, T. N.: A spectrally formulated finite element for flexural wave propagation in beams. Int. J. Anal. Exp. Modal Analysis 5, 13-23 (1990).
6. Gopalakrishnan, S., Martin, M. T., Doyle, J. F.: A matrix methodology for spectral analysis of wave propagation in multiply connected Timoshenko beams. J. Sound Vibr. 158, 11-24 (1992).
7. Martin, M. T., Gopalakrishnan, S., Doyle, J. F.: Wave propagation in multiply connected deep waveguides. J. Sound Vibr. 174, 521-538 (1994).
8. Roy Mahapatra, D., Gopalakrishnan, S., Shankar, T. S.: Spectral-element-based solution for wave propagation analysis of multiply connected unsymmetric laminated composite beams. J. Sound Vibr. 237, 819-836 (2000).
9. Roy Mahapatra, D., Gopalakrishnan, S.: A spectral finite element model for analysis of axial- flexural-shear coupled wave propagation in laminated composite beams. Compos. Struct. 59, 67-88 (2003).
10. Nag, A., Roy Mahapatra, D., Gopalakrishnan, S., Sankar, T. S.: A spectral finite element with embedded delamination for modeling of wave scattering in composite beams. Compos. Sci. Technol., 63, 2187-2200 (2003).
11. Roy Mahapatra, D., Gopalakrishnan, S.: A spectral finite element for analysis of wave propagation in uniform composite tubes. J. Sound Vibr. (in press).
12. Rizzi, S. A.: A spectral analysis approach to wave propagation in layered solids. Ph.D. Diss. Purdue University (1989).
13. Rizzi, S. A., Doyle, J. F.: Force identification for impact problem on a half plane. In: Computational techniques for contact, impact, penetration and perforation of solids (Schwer et al., eds.) AMD 103, ASME, pp. 163-182 (1989).
14. Rizzi, S. A., Doyle, J. F.: Force identification for impact of a layered system. In: Computational aspects of contact, impact and penetration, pp. 222-241. Elmepress International 1991.
15. Doyle, J. F.: Wave propagation in structures. Berlin: Springer 1997.
16. Thomson, W. T.: Transmission of elastic waves through stratified media. J. Appl. Phys. 21, 89-93 (1950).
17. Haskell, N. A.: The dispersion of surface waves in multi-layered media. Bull. Seism. Soc. Am. 43, 17-34 (1953).
18. Kennett, B. L. N.: Seismic wave propagation in stratified media. Cambridge: Cambridge University Press 1983.
19. Lysmer, J.: Lumped mass method for Rayleigh waves. Bull. Seism. Soc. Am. 43, 17-34 (1970).
20. Kausel, E., Rosset, J. M.: Stiffness matrices for layered soils. Bull. Seism. Soc. Am. 71, 1743-1761 (1981).
21. Kausel, E.: Thin-layer method: formulation in time domain. Int. J. Num. Meth. Engng 37, 927-941 (1994).
22. Kausel, E.: Dynamic point sources in laminated media via the thin-layer method. Int. J. Solids Struct. 36, 4725-4742 (1999).
23. Rose, J. L.: Ultrasonic waves in solid media. Cambridge: Cambridge University Press 1999.
24. Solie, L. P., Auld, B. A.: Elastic waves in free anisotropic plates. J. Acoust. Soc. Am. 54, 50-64 (1973).
25. Chakraborty, A., Gopalakrishnan, S.: A higher-order spectral element wave propagation analysis in functionally graded materials. Int. J. Solids Struct. (submitted).
26. Chakraborty, A., Gopalakrishnan, S.: A spectrally formulated finite element for wave propagation analysis in layered composite media. Int. J. Solids Struct. (accepted).
27. Reddy, J. N., Chin, C. D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Thermal Stresses 26, 593-626 (1998).
28. Praveen, G. N., Reddy, J. N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35, 4457-4476 (1998).
29. Reddy, J. N.: Analysis of functionally graded plates. Int. J. Num. Meth. Engng 47, 663-684 (2000).
30. Gong, S. W., Lam, K. Y., Reddy, J. N.: The elastic response of functionally graded cylindrical shells to low-velocity impact. Int. J. Impact Engng 22, 397-417 (1999).
31. Liu, G. R., Tani, J., Ohyoshi, T.: Lamb waves in a functionally gradient material plate and its transient response. Part 1: Theory, Part 2: Calculation results. Trans. Japan Soc. Mech. Eng. 57A, 131-142 (1991).
32. Liu, G. R., Tani, J., Ohyoshi, T., Watanabe, K.: Transient waves in anisotropic laminated plates, Part 1: Theory; Part 2: Applications. J. Vibr. Acoust. 113, 230-239 (1991).
33. Liu, G. R., Tani, J.: SH surface waves in functionally gradient piezoelectric material plates. Trans. Japan Soc. Mech. Eng. 58A, 504-507 (1992).
34. Liu, G. R., Tani, J.: Surface waves in functionally gradient piezoelectric plates. ASME J. Vibr. Acoustics 116, 440-448 (1994).
35. Ohyoshi, T., Sui, G. J., Miuro, K.: Using of stacking model of the linearly inhomogeneous layers elements. Proc. ASME Aerospace Division 52, 101-106 (1996).
36. Liu, G. R., Han, X., Lam, K. Y.: Stress wave in functionally gradient materials and its use for material characterization. Composite Part B30, 383-394 (1999).
37. Bruck, H. A.: A one-dimensional model for designing functionally graded materials to manage stress waves. Int. J. Solids Struct. 37, 6383-6395 (2000).
38. Liu, G. R., Han, X., Lam, K. Y.: An integration technique for evaluating confluent hypergeometric functions and its application to functionally graded materials. Comp. Struct. 79, 1039-1047 (2001).
39. Han, X., Liu, G. R., Xi, Z. C., Lam, K. Y.: Characteristics of waves in a functionally graded cylinder. Int. J. Num. Meth. Engng 53, 653-676 (2002).
40. Han, X., Liu, G. R., Lam, K. Y.: Transient waves in plates of functionally graded materials. Int. J. Num. Meth. Engng 52, 851-865 (2002).
41. Han, X., Liu, G. R.: Effects of SH waves in a functionally graded plate. Mech. Res. Comm. 29, 327-338 (2002).
42. Santarea, M. H., Thamburaj, P., Gazonasb, G. A.: The use of graded finite elements in the study of elastic wave propagation in continuously nonhomogeneous materials. Int. J. Solids Struct. (in press).
43. Berezovski, A., Engelbrecht, J., Maugin, G. A.: Numerical simulation of two-dimensional wave propagation in functionally graded materials. Eur. J. Mech. - A/Solids 22, 257-265 (2003).
44. Chakraborty, A., Gopalakrishnan, S.: Various numerical techniques for analysis of longitudinal wave propagation in inhomogeneous one-dimensional waveguides. Acta Mech. 162, 1-27 (2003).
45. Chakraborty, A., RoyMahapatra D., Gopalakrishnan, S.: Finite element simulation of BAW propagation in inhomogeneous plate due to piezoelectric actuation. Lecture Notes in Computer Science 2668, pp. 715-724 (2003).
46. Chakraborty, A., Gopalakrishnan, S., Reddy, J. N.: A new beam finite element for the analysis of functionally graded materials. Int. J. Mech. Sci. 45, 519-539 (2003).
47. Chakraborty, A., Gopalakrishnan, S.: A spectrally formulated finite element for wave propagation analysis in functionally graded beams. Int. J. Solids Struct. 40, 2421-2448, (2003).
48. Chakraborty, A., Gopalakrishnan, S.: Force identification in a FGM plate using truncated response. AIAA 2003-1590, 44th AIAA/ASME/ASCE/AHS SDM Conference, Norfolk, Virginia, April 7-10 (2003).
49. Chakraborty, A., Gopalakrishnan, S.: A new spectral element for the analysis of wave propagation in inhomogeneous layered media AIAA J. (submitted).
50. Caviglia, G., Morro, A.: Inhomogeneous waves in solids and fluids. Singapore: World Scientific 1992.
51. Viktorov, I. A.: Rayleigh and Lamb waves. New York: Plenum Press 1967.
52. Nayfeh, A. H.: Wave propagation in layered anisotropic media with application to composites. Amsterdam: North Holland 1995.
53. Verdict, G. S., Gien, P. H., Burger, C. P.: Finite element study of Lamb wave interactions with holes and through thickness defects in thin metal plates. NDT & E Int. 29, 62 (1996).
54. Veidt, M., Liub, T., Kitipornchai, S.: Modelling of Lamb waves in composite laminated plates excited by interdigital transducers. NDT & E International 35, 437-447 (2002).
55. Moulin, E., Assaad, J., Delebarre, C., Grondel, S., Balageas D.: Modeling of integrated Lamb waves generation systems using a coupled finite element normal mode expansion method. Ultrasonics 38, 522-526 (2000).
56. Zhao, G., Rose, J. L.: Boundary element modeling for defect characterization potential in a wave guide. Int. J. Solids Struct. 40, 2645-2658 (2003).
57. Sol, H., Hua, H., De Visscher, J., Vantomme, J., De Wilde, W. P.: A mixed numerical/ experimental technique for the nondestructive identification of the stiffness properties of fibre reinforced composite materials. NDT & E International 30, 85-91 (1997).
58. Kim, S. K., Jung, B. S., Kim, H. J., Lee, W.: Inverse estimation of thermophysical properties for anisotropic composite. Exp. Th. Fl. Sci. 27, 697-704 (2003).
59. Al-Khoury, R., Kasbergen, C., Scarpas, A., Blaauwendraad, J.: Spectral element technique for efficient parameter identification of layered media, Part I: Forward calculation. Int. J. Solids Struct. 38, 1605-1623(2001).
60. Al-Khoury, R., Kasbergen, C., Scarpas, A., Blaauwendraad, J.: Spectral element technique for efficient parameter identification of layered media, Part 11: Inverse calculation. Int. J. Solids Struct. 38, 8753-8772 (2001).
61. Nakamura, T., Wang, T., Sampath, S.: Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Mater. 48, 4293-4306 (2000).
62. Han, X., Liu, G. R., Lam, Y.: A quadratic layer element for analyzing stress waves in FGMs and its application in material characterization. J. Sound Vibr. 236, 307-321 (2000).
63. Liu, G. R., Han, X., Xu, Y. G., Lam, K. Y.: Material characterization of functionally graded material by means of elastic waves and a progressive learning neural network. Comp. Sci. Tech. 61, 1401-1411 (2001).
64. Liu, G. R., Han, X., Lam, K. Y.: A combined genetic algorithm and nonlinear least square method for material characterization using elastic waves. Comp. Meth. Appl. Mech. Engng 191, 1909-1921 (2002).
65. Doyle, J. F.: Further developments in determining the dynamic contact law. Exp. Mech. 24, 265- 270 (1984).
66. Doyle, J. F.: Force identification from dynamic response of a bi-material beam. Exp. Mech. 33, 64-69 (1993).
67. Doyle, J. F.: Determining the contact force during transverse impact of plates. Exp. Mech. 27, 68- 72 (1987).
68. Doyle, J. F.: Experimentally determining the contact force during the transverse impact of orthotropic plates. J. Sound Vibr. 118, 441-448 (1987).
69. Reddy, J. N.: Mechanics of laminated composite plates. Boca Raton: CRC Press 1996.
70. Golub, G., van Loan, C.: Matrix computation. Baltimore: John Hopkins University Press 1996.
71. Powell, M. J. D.: A Fortran subroutine for solving systems of nonlinear algebraic equations. In: Numerical methods for nonlinear algebraic equations (Rabinowitz, P., ed.), chap. 7, 115-161 (1970).