Coupling of experimentally validated electroelastic dynamics and mixing rules formulation for macro-fiber composite piezoelectric structures

Abstract

Piezoelectric structures have been used in a variety of applications ranging from vibration control and sensing to morphing and energy harvesting. In order to employ the effective 33-mode of piezoelectricity, interdigitated electrodes have been used in the design of macro-fiber composites which employ piezoelectric fibers with rectangular cross section. In this article, we present an investigation of the two-way electroelastic coupling (in the sense of direct and converse piezoelectric effects) in bimorph cantilevers that employ interdigitated electrodes for 33-mode operation. A distributed-parameter electroelastic modeling framework is developed for the elastodynamic scenarios of piezoelectric power generation and dynamic actuation. Mixing rules (i.e. rule of mixtures) formulation is employed to evaluate the equivalent and homogenized properties of macro-fiber composite structures. The electroelastic and dielectric properties of a representative volume element (piezoelectric fiber and epoxy matrix) between two neighboring interdigitated electrodes are then coupled with the global electro-elastodynamics based on the Euler–Bernoulli kinematics accounting for two-way electromechanical coupling. Various macro-fiber composite bimorph cantilevers with different widths are tested for resonant dynamic actuation and power generation with resistive shunt damping. Excellent agreement is reported between the measured electroelastic frequency response and predictions of the analytical framework that bridges the continuum electro-elastodynamics and mixing rules formulation.