Size-dependent parametrisation of active vibration control for periodic piezoelectric microplate coupled systems: A couple stress-based isogeometric approach

Abstract

We propose a couple stress based isogeometric analysis (IGA) model for the study of active vibration control in periodic piezoelectric microplate coupled systems. The model integrates the modified couple stress elasticity, which accounts for microstructure effects but necessitates the implementation of at least C1 continuous finite elements, and the IGA finite element, which fulfils the element continuity criterion. This complementary combination enables size-dependent parametrisation of the feedback vibration controller for piezoelectric microplate coupled systems. Therefore, we examined a two-parameter control relationship that modulates the voltage gain within the sensor-to-actuator circuit in relation to mass and stiffness with the account for varying problem sizes. To assess the vibration properties of the microplate system, we performed bandgap analysis and compared the results to transient responses. Additionally, we investigated the impact of couple stress on bandgaps and devised a computational methodology for determining optimal control parameters concerning the desired vibration bandgaps. Our computational procedure serves as valuable tool for assisting in the parametrisation of feedback vibration controllers in microplates with tunable vibration bandgaps.