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

Abstract

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 1cosh 2 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.

New Shear Horizontal (SH) Surface-Plasmon-Polariton-like Elastic Surface Waves for Sensing Applications

“…Our former research [ 30 ] on elastic surface waves propagating in conventional elastic waveguides showed that SH surface waves, such as Love surface waves [ 31 ], share many common properties with waves in other domains of physics, such as TM (Transverse Magnetic) modes in optical planar waveguides or wave function of quantum particles in a potential well. However, the present paper was mostly influenced by recent developments in the domain of elastic metamaterials and SPP electromagnetic surface waves propagating at the metal-dielectric interface [ 32 ].…”

Properties and Applications of Love Surface Waves in Seismology and Biosensors

“…As a consequence, using Eqs. 7and (10), one can show [8,[15][16][17][18][19]] that group v g and phase v p velocities of the Love surface wave are connected via the following algebraic equation:…”

“…humidity of air[9]; spatial distribution of elastic parameters in solid functionally graded materials (FGM)[10];…”

Impact of losses on Love wave propagation in multilayered composite structures loaded with a Newtonian liquid

“…Second, the energy of Love waves attains high densities in guiding surface layers. This property is crucial in successful development of Love wave sensors working generally in a liquid environment (Kiełczyński, 1997;Kiełczyński and Szalewski, 2011;Kiełczyński et al, 2012Kiełczyński et al, , 2014Kiełczyński et al, , 2015. Last but not least, the analytical formulas describing propagation of Love surface waves are relatively compact, which enable drawing clear physical conclusions.…”