Analysis of Lamb wave propagation in a functionally graded piezoelectric small-scale plate based on the modified couple stress theory

Abstract This work focuses on the propagation characteristics of Lamb-type waves in a functionally graded piezoelectric (FGP) small-scale plate. Based on the modified couple stress theory, Legendre orthogonal polynomial method (LOPM) is extended to perform the solving process. By introducing the rectangular window function and expanding the electric potential and displacement vectors to Legendre orthogonal polynomial series, the governing equations satisfying the electric-open and electric-short circuit boundary conditions are presented respectively. The solutions based on the global matrix method (GMM) are deduced to verify the correctness of this extended LOPM. Since there is no layered processing, the extended LOPM provides a more realistic analysis model for the FGP small-scale plate and has a high computational efficiency. Furthermore, the dispersion characteristics, stress and electromechanical coupling factor are investigated in details. Results show that the size and piezoelectric effect increase the phase velocity, and the piezoelectricity suppresses the influence of couple stress on the dispersion characteristics. The Lamb wave phase velocities of the first and second modes with different Ly always converge to two fixed values at different convergence speeds. The conclusions obtained can be applied to the design and dynamic response evaluation of composite small-scale structures.