Study of the dynamic electro-mechanical and microstructural behaviour on the elastic wave in FGM/FGPM composite structure: WKB asymptotic approach

This paper presents a theoretical investigation of the horizontally polarized shear wave in a composite structure. The assumed composite is composed of Functionally graded piezoelectric material (FGPM) layer constrained between an FGM (Functionally graded material) layer and a couple stress half-space with size-dependent microstructural effect. The variation in rigidities and densities are considered parabolic and linear in the upper and constrained layers, respectively. An analytical WKB (Wentzel–Kramers–Brillouin) asymptotic approach has been adopted for obtaining the dispersion relation. Also, a finite difference scheme (FDS) has been introduced to calculate the phase velocity and group velocity of the SH-wave. If waves travel in the time domain, it is necessary to check the accuracy and stability requirements. So that FDS has been adopted because of its accuracy, reliability, and flexibility. For the purpose of numerical calculation, three sets of FGPMs are considered namely, PZT−4, PZT−5H ceramic, and BaTiO3 ceramic. Graphs have been plotted by means of dimensionless phase velocity against dimensionless wave number to show the effect of various parameters on the propagation of SH-wave. Numerical results demonstrated the accuracy and versatility of the phase and group velocity depending on the stability ratio of the FDS.