Influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces

• Reflection coefficients are dependent of apparent wavenumber for imperfect interface.
• The energy reflection and transmission coefficients are calculated.
• The norm energy flux conservation is used to validate the numerical results.
• The dielectrically imperfect interface is studied in the reflection and refraction problem.
• Six kinds of imperfect interfaces and three kinds of incident waves are considered.

The influences of mechanically and dielectrically imperfect interfaces on the reflection and transmission waves between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation. Then, six kinds of imperfect interfaces are considered. These imperfect interfaces include: the mechanically compliant, dielectrically weakly conducting imperfect interface; the mechanically compliant, dielectrically highly conducting imperfect interface; the grounded metallized interface and the low-dielectric interface and their mechanical counterpart, namely, the fixed interface and the slippery interface. These imperfect interface conditions are required to be satisfied by four sets of waves, namely, the quasi-longitudinal wave (QP), the quasi-transverse wave (QSV), the shear horizontal wave (SH) which is decoupled to other waves and the electric-acoustic wave (EA). The algebraic equations resulting from the imperfect interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the reflection and transmission coefficients in terms of the energy flux ratio. The numerical results are obtained for the incident QP wave, the incident QSV wave and the incident SH wave and are validated by the energy conservation principle. The effects of these imperfect interfaces are discussed based on the numerical results. The present study provides useful information for the detection of imperfect interface.