Analysis of reflection and transmission phenomenon at distinct bonding interfaces in a rotating pre-stressed functionally graded piezoelectric-orthotropic structure

Abstract

The present mathematical study analyzes the reflection and transmission phenomenon of a plane wave being incident at the distinct types of separating interfaces in a rotating pre-stressed structure with two semi-infinite media comprised of functionally graded piezoelectric-orthotropic (FGPO) materials. The effects of pre-stresses, rotation, and functional gradients along with six different types of boundaries viz. Normal stiffness boundary (NSB), Transverse stiffness boundary (TSB), Electric imperfection boundary (EIB), Complete debonded boundary (CDB), Slip boundary (SB), and Welded contact boundary (WCB) on reflection coefficients (RCs) of reflected qP, qSV, and EA waves and transmission coefficients (TCs) of transmitted qP, qSV, and EA waves have been examined with a comparative approach. Comparison of the obtained result with that of the case when rotating pre-stressed structure with two semi-infinite media is constituted of lesser anisotropic functionally graded transversely isotropic piezoelectric (FGTIP) materials is also carried out. To validate the findings energy-partitions of reflected and transmitted waves for both the cases of the structures have been computed and shown to observe the Law of conservation of energy. Further, on considering a grazing incident of qP wave in both the cases of structure, RCs and TCs for reflected and transmitted qSV waves and EA waves become zero, whereas the RC for reflected and TC of transmitted qP wave gets out of phase. Some important peculiarities have also been highlighted through numerical results, which serve as a salient feature of the study.