Finite difference based vibration simulation analysis of a segmented distributedpiezoelectric structronic plate system

Abstract

Electrical modeling of piezoelectric structronic systems by analog circuits has thedisadvantages of huge circuit structure and low precision. However, studies of electricalsimulation of segmented distributed piezoelectric structronic plate systems (PSPSs) byusing output voltage signals of high-speed digital circuits to evaluate the real-time dynamicdisplacements are scarce in the literature. Therefore, an equivalent dynamic modelbased on the finite difference method (FDM) is presented to simulate the actualphysical model of the segmented distributed PSPS with simply supported boundaryconditions. By means of the FDM, the four-ordered dynamic partial differentialequations (PDEs) of the main structure/segmented distributed sensor signals/controlmoments of the segmented distributed actuator of the PSPS are transformed tofinite difference equations. A dynamics matrix model based on the Newmark-β integration method is established. The output voltage signal characteristics of the lower modes (m ≤ 3,n ≤ 3) with different finite difference mesh dimensions and different integration time steps areanalyzed by digital signal processing (DSP) circuit simulation software. The control effectsof segmented distributed actuators with different effective areas are consistent with theresults of the analytical model in relevant references. Therefore, the method of digitalsimulation for vibration analysis of segmented distributed PSPSs presented in this papercan provide a reference for further research into the electrical simulation of PSPSs.