An asymptotic approximation of Love wave frequency in a piezo-composite structure: WKB approach

Abstract

This paper proposes an asymptotic approximation solution for the propagation of Love-type surface waves in a smart composite structure involving functionally graded piezoelectric material (FGPM). The considered structure is a three-layered system in which the uppermost piezoelectric (PE) layer is accomplished by an FGPM layer and piezomagnetic (PM) substrate. The distribution of material coefficients in FGPM layer is considered in two different manners: exponential and linear, along with the x-axis. The Wentzel-Kramers-Brillouin (WKB) asymptotic method is adopted to solve the differential equations. Frequency equations are derived for electrically and magnetically open and short circuit cases. Variation of phase velocity, group velocity and electromechanical coupling factor versus the wave number has been distinctly marked. Influence of different parameters (like layer width, material gradient) on phase velocity curve of different modes has been shown graphically. Comparison between phase velocity and group velocity has been also demonstrated through graphs. This study finds its application toward designing and optimization of Seismic Acoustic Wave (SAW) devices, ultrasonic transducer and Love wave sensors.