Modelling of love-type wave propagation in piezomagnetic layer over a lossy viscoelastic substrate: Sturm–Liouville problem

Abstract

We propose an analytical solution for the propagation of Love-type surface seismic waves in a piezo-composite smart structure. A model describing the Love-type wave propagation in the piezomagnetic waveguide is considered. The model is comprised of piezomagnetic layer lying on a lossy viscoelastic substrate. In this regard a direct Sturm–Liouville problem has been formulated and solved. Complex dispersion equations have been derived for both magnetically open and short cases. For each case we have obtained two nonlinear equations containing two unknowns and various parameters. These nonlinear equations are solved using suitable numerical method implemented in Mathematica 9.0 software. Further, the obtained frequency relations are matched with the classical case of Love wave to validate the problem. The influence of different parameters (thickness of the layer, frequency, piezomagnetic coefficient and elastic parameter) on the phase velocity and attenuation of Love-type waves are discussed and delineated through graphs. The results have immense applications in non-destructive evaluation, designing of viscosity sensors, SAW devices, biosensors and chemosensors.