The reverberation-ray matrix and transfer matrix analyses of unidirectional wave motion

Wave Motion

Volumn 44, Issue 6, 2007, Pages 419-438

  Pao, Yih Hsing ^a   Chen, Wei Qiu ^b   Su, Xian Yue ^c  

^a ZHEJIANG UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY   (China)

^c PEKING UNIVERSITY   (China)

Author keywords

Fourier synthesis of transient waves; Method of reverberation ray matrix; Method of transfer matrix; State equation; Unidirectional wave

Indexed keywords

DIFFERENTIAL EQUATIONS; ELASTIC WAVES; FOURIER TRANSFORMS; REVERBERATION; TRANSFER MATRIX METHOD;

FOURIER SYNTHESIS; REVERBERATION-RAY MATRIX; TRANSIENT WAVES; UNIDIRECTIONAL WAVE; WAVE MOTION;

SEISMIC WAVES;

DIFFERENTIAL EQUATIONS; ELASTIC WAVES; FOURIER TRANSFORMS; REVERBERATION; SEISMIC WAVES; TRANSFER MATRIX METHOD;

BOUNDARY CONDITION; FOURIER TRANSFORM; MATRIX; TRANSFER FUNCTION; WAVE PROPAGATION;

EID: 34249948610     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2007.02.004     Document Type: Review

References (34)

1. Levine H. Unidirectional Wave Motions (1978), North-Holland, Amsterdam
2. Gilbert F., and Backus G.E. Propagator matrices in elastic wave and vibration problems. Geophysics 31 (1966) 326-332
3. Frazer R.A., Duncan W.J., and Collar A.R. Elementary Matrices and Some Applications to Dynamics and Differential Equations (1938), Cambridge University Press, Cambridge
4. Myklestad N.O. A new method of calculating natural modes of uncoupled bending vibration. J. Aeronaut. Sci. 1 (1944) 153-162
5. Thomson W.T. Matrix solution for the vibration of non-uniform beams. J. Appl. Mech. 17 (1950) 337-339
6. Thomson W.T. Transmission of elastic waves through a stratified solid medium. J. Appl. Phys. 21 (1950) 89-93
7. Haskell N. The dispersion of surface waves on multilayered media. Bull. Seismic Soc. Am. 43 (1953) 17-34
8. Pestel E.C., and Leckie F.A. Matrix Methods in Elasto Mechanics (1963), McGraw-Hill, New York
9. Howard S.M., and Pao Y.-H. Analysis and experiments on stress waves in planar trusses. J. Eng. Mech. 124 (1998) 884-891
10. Pao Y.-H., Keh D.-C., and Howard S.M. Dynamic response and wave propagation in plane trusses and frames. AIAA J. 37 (1999) 594-603
11. Pao Y.-H., Su X.Y., and Tian J.Y. Reverberation matrix method for propagation of sound in a multilayered liquid. J. Sound Vib. 230 (2000) 743-760
12. Su X.Y., Tian J.Y., and Pao Y.-H. Application of the reverberation-ray matrix to the propagation of elastic waves in a layered solid. Int. J. Solids Struct. 39 (2002) 5447-5463
13. Chen J.-F., and Pao Y.-H. Effects of causality and joint conditions on method of reverberation-ray matrix. AIAA J. 41 (2003) 1138-1142
14. Pao Y.-H., and Sun G. Dynamic bending strains in planar trusses with pinned or rigid joints. J. Eng. Mech. 129 (2003) 324-332
15. Nagem R.J., and Williams J.H. Dynamic analysis of large space structure using transfer matrices and joint coupling matrices. Mech. Struct. Mach. 17 (1989) 349-371
16. Y.-H. Pao, G.H. Nie, D.-C. Keh, Dynamic response and wave propagation in three-dimensional framed structures, submitted for publications.
17. Lin H.P., and Chang S.C. Free vibration analysis of multi-span beams with intermediate flexible constraints. J. Sound Vib. 281 (2005) 155-169
18. Berger B.S., and Shore S. Dynamic response of lattice-type structures. Proceedings of ASCE, J. Eng. Mech. Div. EM2, 89 (1963) 47-70
19. Lin Y.K., and McDaniel T.J. Dynamics of beam-type periodic structures. J. Eng. Ind. 91 (1969) 1133-1141
20. Lin Y.K., and Donaldson B.K. A brief survey of transfer matrix techniques with special reference to the analysis of aircraft panels. J. Sound Vib. 10 (1969) 103-143
21. Kennett B.L.N. Seismic Wave Propagation in Stratified Media (1983), Cambridge University Press, Cambridge
22. Fellipa C.A. A historical outline of matrix structural analysis: a play in three acts. Comput. Struct. 79 (2001) 1313-1324
23. Adler E.L. Matrix methods applied to acoustic waves in multilayers. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37 (1990) 485-490
24. Lowe M.J.S. Matrix techniques for modeling ultrasonic waves in multilayered media. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 (1995) 525-542
25. Sasmal S., and Ramanjaneyulu K. Transfer matrix method for construction phase analysis of incrementally launched prestressed concrete bridges. Eng. Struct. 28 (2006) 1897-1910
26. Hsieh S.C., Chen J.H., and Lee A.C. A modified transfer matrix method for the coupling lateral and torsional vibrations of symmetric rotor-bearing systems. J. Sound Vib. 289 (2006) 294-333
27. Doyle J.F. Wave Propagation in Structures. second ed. (1997), Springer, New York
28. Wang L.G., and Rokhlin S.I. Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media. Ultrasonics 39 (2001) 413-424
29. Chapman C.H. Yet another elastic plane-wave, layer-matrix algorithm. Geophys. J. Int. 154 (2003) 212-223
30. Yong Y., and Lin Y.K. Dynamics of complex truss-type space structures. AIAA J. 28 (1990) 1250-1258
31. Luongo A., and Romeo F. Real wave vectors for dynamic analysis of periodic structures. J. Sound Vib. 279 (2005) 309-325
32. Wang L.G., and Rokhlin S.I. Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium. J. Mech. Phys. Solids 52 (2004) 2473-2506
33. Clough R.W., and Penzien J. Dynamics of Structures. 3rd ed. (1995), McGraw-Hill, New York
34. S. M. Howard, Transient Stress Waves in Trusses and Frames, Doctoral thesis, Cornell University, 1990.