Scattering of anti-plane shear waves by a partially debonded magneto-electro-elastic circular cylindrical inhomogeneity

Abstract

This paper presents an analysis of the scattering of anti-plane shear waves by a single piezoelectric cylindrical inhomogeneity partially bonded to an unbounded piezomagnetic matrix. The anti-plane governing equations for linearly magneto-electro-elastic medium are reduced to one Helmholtz and two Laplace's equations. The fields of scattered waves are obtained by means of the wave function expansion method on condition that the bonded interface is perfect. The region of the debonding is modeled as an interface crack with noncontacting faces. The magneto-electric permeable boundary conditions are adopted, i.e. the normal electric displacement, electric potential, normal magnetic induction and magnetic potential are continuous across the crack faces. The crack opening displacement is represented by Chebyshev polynomials and a system of equations is derived and solved for the unknown coefficients. Some examples are calculated and the results are figured. The results show that the COD increases as k 1 a becomes larger initially, then the COD decreases as k 1 a becomes larger still, where k 1 is the incident wave number and a the inhomogeneity radius. The COD gets smaller as the piezoelectric coefficient of the inhomogeneity increases.