Model refinements with experimental validation in piezoelectric plate actuators

The axisymmetric vibration analysis of circular plates with piezoelectric layers and step changes in plate thickness is conducted. For the chosen configurations, it is necessary to solve a coupled system of differential equations for extensional and flexural vibration to obtain accurate modal results. The adopted computational approach is based upon the classical transfer matrix method. Instead of employing analytical solutions in the form of e.g. Bessel functions, matrix exponentials of the system matrix are directly computed in the transfer matrices for finding highly accurate solutions. The developed approach has enabled the complete quantitative modal analysis in piezoelectric actuators. The procedure is firstly verified against available analytical results for natural frequencies and modes shapes in circular homogeneous plates, and by using finite element simulations for plates with asymmetric step changes. Ultimately, the developed approach is validated against experimental results of relevance to applications in piezoelectric synthetic jet actuation. The obtained numerical results for modal parameters and frequency response functions are in excellent agreement with the available analytical results, and with previous and newly presented in the paper experimental data, when considering the inherent uncertainty in parameter values. Based on extensive experimental results, realistic damping is introduced in the model of piezoelectric plate actuators. Importantly, it is shown that solutions of high accuracy can be obtained by a more general coordinate system than that traditionally linked to the plate neutral plane(s).