Kirchhoff plate theory-based electromechanically-coupled analytical model considering inertia and stiffness effects of a surface-bonded piezoelectric patch

Abstract

As a compact and durable design concept, piezoelectric energy harvesting skin (PEH skin) has been recently proposed for self-powered electronic device applications. This study aims to develop an electromechanically-coupled analytical model of PEH skin considering the inertia and stiffness effects of a piezoelectric patch. Based on Kirchhoff plate theory, Hamilton's principle is used to derive the electromechanically-coupled differential equation of motion. Due to the geometric discontinuity of the piezoelectric patch, the Rayleigh-Ritz method is applied to calculate the natural frequency and corresponding mode shapes. The electrical circuit equation is derived from Gauss's law. Output voltage is estimated by solving the equation of motion and electrical circuit equation, simultaneously. For the purpose of evaluating the predictive capability, the results of the electromechanically-coupled analytical model are compared with those of the finite element method in a hierarchical manner. The outstanding merits of the electromechanically-coupled analytical model of PEH skin are three-fold: (1) consideration of the inertia and stiffness effects of the piezoelectric patches; (2) physical parameterization between the two-dimensional mechanical configuration and piezoelectric transduction; (3) manipulability of the twisting modes of a cantilever plate with a small aspect ratio.