Group and Phase Velocity of Love Waves Propagatingin Elastic Functionally Graded Materials

Journal title

Archives of Acoustics




No 2

Publication authors


surface Love waves, group velocity, phase velocity, functionally graded materials, profiles ofelastic constants, direct Sturm-Liouville problem

Divisions of PAS

Nauki Techniczne


This paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomo- geneous 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 nonhomoge- neous 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 mate- rials.


Committee on Acoustics PAS, PAS Institute of Fundamental Technological Research, Polish Acoustical Society


ISSN 0137-5075 ; eISSN 2300-262X