ANSYS Modelling of Piezoelectric Smart Beam using Ritz Vector Method and Sub-structuring Analysis

Abstract

Finite element analysis (FEA) is an important tool for smart structure modelling, particularly in the context of piezoelectric beams. A key challenge in such modelling is the derivation of electro-elastic coupling, which explains how these structures respond mechanically to electrical loading. Traditional methods rely on intricate shape functions that encompass both electrical and mechanical degrees of freedom, rendering the process complex.

In this study, an innovative approach—the so-called Ritz vector method— which facilitates modelling of the system based on loading effect is implemented to simplify electro-elastic coupling calculations. The method previously applied in MSC Nastran with a thermal analogy system and validated experimentally is now implemented in the widely accessible ANSYS software. By harnessing ANSYS’ robust piezoelectric capabilities and sub-structuring analysis for matrix extraction, the essential piezoelectric coupling and dielectric matrices are derived for piezoelectric stack and patch actuator driven cantilevered beams.

Subsequently, state space models of these smart structures are constructed using MATLAB and results are compared with ANSYS FEA static and dynamic response. Active Disturbance Rejection Control (ADRC) was implemented on the modelled beams and results show significant suppression of free vibration due to impulse excitation of the tip. This work portrays the potential of the Ritz vector method, a powerful yet underexplored tool that simplifies electro-elastic coupling calculations for piezoelectric smart structures.