Dynamic performance of unimorph piezoelectric bending actuators

Abstract

Piezoelectric bending actuators utilise the inverse piezoelectric effect to convert input electric energy to useful mechanical work. A comprehensive analytical model of the dynamic electromechanical behaviour of a unimorph piezoelectric actuator has been developed and successfully validated against experimental data. The model provides a mapping between force, displacement, voltage and charge. Damping is modelled using experimental data. Experimental validation is based on measurement of mode shape and frequency response of a series of unimorph beams of varying length but of the same thickness and material. The experimental frequency response is weakly nonlinear with excitation voltage, with a reduction in natural frequency and increase in damping with increasing excitation amplitude. An expression for the electromechanical coupling factor has been extracted from the analytical model and is used as the objective for parametric design studies. The design parameters are thickness and Young’s modulus ratios of the elastic and piezoceramic layers, and the piezoelectric constant k31. The operational design point is defined by the damping ratio. It is found that the relative variation in the electromechanical coupling factor with the design parameters for dynamic operation is similar to static operation; however, for light damping, the magnitude of the peak electromechanical coupling factor will typically be an order of magnitude greater than that of static operation. For the actuator configuration considered in this study, it is shown that the absolute variation in electromechanical coupling factor with thickness ratio for dynamic operation is same as that for static operation when the damping ratio is 0.44.