The reflection and transmission of waves at an imperfect interface between two weakly nonlocal piezoelectric half-spaces and inverse problem

Abstract

In this paper, the problem of reflection and transmission of an incident qP wave between two nonlocal piezoelectric half-spaces is studied based on the weakly nonlocal theory proposed recently. Firstly, the system of equation for the problem of a harmonic plane wave propagating in a transversely isotropic piezoelectric medium is briefly stated following the weakly nonlocal theory. This theory ensures the well-posedness of the plane wave problems and provides the exact expressions for the characteristic equation and the nonlocal eigenvectors of a harmonic plane wave in explicit forms. Secondly, the problem of reflection and transmission of an incident qP wave at an imperfect interface between two half-spaces is considered. The imperfect interface includes both mechanically and dielectrically weakly imperfect properties. The imperfect nonlocal boundary conditions are used for three sets of waves, namely the quasi-longitudinal wave (qP), the quasi-transverse wave (qSV) and the electroacoustic wave (EA) to obtain the amplitude ratios of the reflection/transmission waves to the incident wave as well as the energy flux ratios. Next, some numerical results are computed to graphically illustrate the effect of nonlocal property and the effect of imperfect interface on the energy flux ratios of the reflection/transmission waves. It is shown that nonlocal property has a considerable effect for incident waves of short wavelength. Finally, a potential application of the present study to estimate the state of imperfect interface is illustrated by some examples of inverse problem using information of energy flux ratios of transmission qP wave. The inverse problems return good and stable results in detecting the normal imperfect and electrical imperfect parameters.