Archives of Acoustics, 40, 2, pp. 273–281, 2015
10.1515/aoa-2015-0030

Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

Piotr KIEŁCZYŃSKI
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Marek SZALEWSKI
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Andrzej BALCERZAK
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

Krzysztof WIEJA
Institute of Fundamental Technological Research, Polish Academy of Sciences
Poland

This paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2 type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.

The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.
Keywords: surface Love waves; group velocity; phase velocity; functionally graded materials; profiles of elastic constants; direct Sturm-Liouville problem.
Full Text: PDF

References

Achenbach, J.D. (1973), Wave propagation in elastic solids, North-Holland, Amsterdam.

Adams, M. (1981), An introduction to optical waveguides. Wiley, Chichester.

Auld, B.A. (1991), Surface acoustic waves and devices, Archives of Acoustics, 16, 11-30.

Bakhvalov, N.S. (1977), Numerical methods: analysis, algebra, ordinary differential equations, Mir, Moscow.

Ciplys, D., Paskauskas, J., Rimeika, R. (1995), Collinear diffraction of guided optical modes by dispersive surface acoustic waves in Z-cut proton –exchanged LiNbO3, SPIE Proceedings, vol. 2643, Acoustooptics and Applications II, October1995, 244-252, doi:10.1117/12.222749.

Gupta S., Majhi, D.K., Kundu, S., Vishwakarma, S.K. (2013), Propagation of Love waves in non-homogeneous substratum over initially stressed heterogeneous half-space, Applied Mathematics and Mechanics (English Edition), 34, 249-258.

Haskell, N.A. (1953), The dispersion of surface waves on multilayered media, Bulletin of the Seismological Society of America, 43, 17-34.

Hirao, M., Sotani, Y., Takami, K., Fukuoka,H. (1981), Love wave propagation in a solid with a cold-worked surface layer, Journal of Nondestructive Evaluation, 2, 51-55.

Kiełczyński, P. (1981), Propagation of surface SH waves in nonhomogeneous media, Journal of Technical Physics, 22, 73-78.

Kiełczyński, P., Pajewski, W. (1989), Inverse method for determining the depth of nonhomogeneous surface layers in elastic solids from the measurements of the dispersion curves of group velocity of surface SH waves, Applied Physics A, 48, 423-429.

Kiełczyński, P., Szalewski, M., Balcerzak, A., Rostocki, A.J., Tefelski, D.B. (2011a), Applications of SH surface acoustic waves for measuring the viscosity of liquids in function of pressure and temperatures, Ultrasonics, 51, 921-924.

Kiełczyński, P., Szalewski, M. (2011b), An inverse method for determining the elastic properties of thin layers using Love surface waves, Inverse Problems in Science and Engineering, 19, 31-43.

Kiełczyński, P., Szalewski, M., Balcerzak, A. (2012a), Effect of a viscous liquid loading on Love wave propagation, International Journal of Solids and Structures, 49, 2314-2319.

Kiełczyński, P., Szalewski, M., Balcerzak, A., Malanowski, A., Siegoczyński, R.M., & Ptasznik, S. (2012b), Investigation of high-pressure phase transitions in DAG (diacylglycerol) oil using the Bleustein-Gulyaev ultrasonic wave method, Food Research International, 49, 60-64.

Kiełczyński, P., Szalewski, M., Balcerzak, A. (2014), Inverse procedure for simultaneous evaluation of viscosity and density of Newtonian liquids from dispersion curves of Love waves, Journal of Applied Physics, 116, 044902 (7 pages).

Kuznetsov, S.V. (2010), Love waves in nondestructive diagnostics of layered composites, Acoustical Physics, 56, 877-892.

Kuznetsov, S.V., Nafasov, A.E. (2011), Horizontal acoustic barriers for protection from seismic waves, Advances in Acoustics and Vibrations, Vol. 2011, Article ID 150310, 8 pages, doi:10.1155/2011/150301.

Tamir, T. (ed), (1975), Integrated Optics, Springer, Berlin.

Thompson, W.T. (1950), Transmission of elastic waves through a stratified solid medium, Journal of Applied Physics, 21, 89-93.

Tournois, P., Lardat, C. (1969), Love wave-dispersive delay lines for wide-band pulse compression, IEEE Trans on Sonics and Ultrasonics, 16, 107-116.

Urbańczyk, M., Jakubik, W. (1997), Devices for measurement of the NO2 concentration in the air by means of surface acoustic waves, Archives of Acoustics, 22, 197-206.

Wang, W., Oh, H., Lee, K., Yang, S. (2008), Enhanced sensitivity of wireless chemical sensor based on Love wave mode, Japanese Journal of Applied Physics, 47, 7372-7379.

Wang, H.M., Zhao, Z.C. (2013), Love waves in a two-layered piezoelectric/elastic composite plate with an imperfect interface, Archives of Applied Mechanics, 83, 43-51.

Water, W., Chen, S.E. (2009), Using ZnO nanorods to enhance sensitivity of liquid sensor, Sensors and Actuators B: Chemical, 136, 371-375.

Zhang, Z., Wen, Z., Wang, C. (2013), Investigation of surface acoustic waves propagating in ZnO-SiO2-Si multilayer structure, Ultrasonics, 53, 363-368.




DOI: 10.1515/aoa-2015-0030

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)