Active tuning of vibration for periodic piezoelectric micro systems: A non-local Mindlin plate finite element approach

Abstract

The present paper is aimed to propose a multi-parameter feedback control method combined with couple stress elasticity to model piezoelectric micro plate coupled systems. The proposed methodology can be used to design controllers for tuning vibration and wave propagation properties of micro scale plates based on coupled piezoelectric sensors and actuators. Specifically, we use a three-parameter relationship that describes the voltage gain within the sensor-to-actuator circuit involving multiple dependence based on mass, damping and stiffness. Consequently, effect of these parameters can be simulated either independently or collectively so as to obtain the optimal control strategy with respect to the required vibroacoustic properties. Meanwhile, since micro plates are involved, the inherent microstructure effects must be accounted for. Hence, the modified couple stress elasto-dynamics is applied and the micro plate model is discretised with a four-node quadrilateral non-conforming element that offers nodal compatibility with high-order theories of elasticity. Based on the proposed numerical methodology, we investigated the feedback control parametrisation for a reference micro plate coupled system which presents significant microstructure effects. Our analysis allowed characterisation of the three control parameters based on their individual effects, and revealed that their combined effect cannot be predicted by considering direct superposition of their individual behaviours. Therefore, the proposed computational methodology provides a convenient solution for the choice and parametrisation of the feedback controller leading to tunable band gap properties of micro scale plate structures.