On the Wave Propagation in Layered Plates of General Anisotropic Media

Authors: K. L. Verma

Abstract:

Analysis for the propagation of elastic waves in arbitrary anisotropic plates is investigated, commencing with a formal analysis of waves in a layered plate of an arbitrary anisotropic media, the dispersion relations of elastic waves are obtained by invoking continuity at the interface and boundary of conditions on the surfaces of layered plate. The obtained solutions can be used for material systems of higher symmetry such as monoclinic, orthotropic, transversely isotropic, cubic, and isotropic as it is contained implicitly in the analysis. The cases of free layered plate and layered half space are considered separately. Some special cases have also been deduced and discussed. Finally numerical solution of the frequency equations for an aluminum epoxy is carried out, and the dispersion curves for the few lower modes are presented. The results obtained theoretically have been verified numerically and illustrated graphically.

Keywords: Anisotropic, layered, dispersion, elastic waves, frequency equations.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332990

References:

[1] S. K. Datta , A. H. Shah ,R.I. Bratton and T. Chakraboty, "Wave Propagation in laminated composite plates", J. Acoust. Soc. Am. Vol. 83(6), 2020-2026, 1989).
[2] N.A. Haskell, "The dispersion of surface waves on multilayered media, Bulletin of the Seismological Society of America 43, 17-34, 1953.
[3] G. R., Liu, Tani, J. T. Ohyoshi and K. Watanabe "Lamb wave propagation in anisotropic laminates". Journal of Applied Mechanics Vol. 57, 923-229, 1990.
[4] E. N. Thrower, "The computation of the dispersion of elastic waves in layered media", J. Sound and Vibrations, 2(3), 210-116, 1965.
[5] L.M. Brekhovskikh, Waves in Layered Media, Academic Press, New York, 1960.
[6] E. Ewing, W.S. Jardetzky, F. Press, Elastic Waves in Layered Media, McGraw-Hill, New York, 1957.
[7] B.L.N. Kennett, Seismic Wave Propagation in Stratified Media, Cambridge University Press, Cambridge, 1983.
[8] A. H. Nayfeh, Wave Propagation in Layered Anisotropic Media with Application to Composites, Applied Mathematics and Mechanics, North- Holland, Amsterdam, 1995.
[9] I. A. Viktorov Rayleigh and Lamb Waves , Plenum , New York, 1967
[10] H. Lamb, "On waves in an Elastic Plate , Proc. R. Soc. London Ser. A93, 114-128, 1917,.
[11] I. Abubakar , "Free Vibration of a transversely isotropic Plate", Quart. J. of Mech. and Appl. Mathematics, Vol. 15, 129-136, 1962.
[12] V. Dayal and V. K. Kinra, "Leaky Lamb waves in anisotropic plate I: An exact solution and experiments", J. Acoust. Soc. Am. Vol. 83(6), 2268- 2276, 1989.
[13] A. H. Nayfeh and D.E.Chimenti, "Free Wave propagation in plates of general anisotropic media", J. applied Mechanics, Vol.87, 881-886, 1989.
[14] K. L. Verma, Propagation of Generalized Free waves in plates of anisotropic media Proc. Second Int. Symp. on Thermal stresses and related Topics, June 1997, pp 99-201.
[15] K. L Verma., Vibrations in Plates of anisotropic media. Proc. of fourth International Conference on Vibrations Problems, Jadavpur University CALCUTTA, INDIA ICOVP-99, November 27-30, 1999, pp39-44.
[16] L. P. Solie and B.A Auld, Elastic Waves in Free Anisotropic Plates, J. Acoust. Soc. Am. 54, 50-65, 1973.
[17] J. L.Synge, "Elastic waves in anisotropic Media", J. Math. Phy.,Vol. 25, 322-334, 1957.
[18] W. T. Thomson, "Transmission of elastic waves through a stratified solid medium", Journal of Applied Physics 21, 89-93, 1950.
[19] Y. Li and R. B. Thompson, "nfluence of anisotropy on the dispersion of guided ultrasonic plate modes", J. Acoust. Soc. Am. Vol. 87, 1911-1931, (1990).
[20] A. H. Nayfeh , "The propagation of horizontally Polarized Shear Waves in Multilayred Anisotropic Media", J. Acoust. Soc. Am. Vol. 89(4), (1989), 2007.