Nonlinear model order reduction of resonant piezoelectric micro-actuators: an invariant manifold approach

TL;DR

This paper introduces a new invariant manifold-based model order reduction method for nonlinear piezoelectric micro-actuators, significantly reducing computational costs while maintaining accuracy validated through simulations and experimental data.

Contribution

It develops a direct parametrisation method for invariant manifolds tailored for nonlinear piezoelectric structures, incorporating hysteretic and electrostrictive effects based on ferroelectric theory.

Findings

Significant reduction in simulation time due to dimensionality reduction.

High accuracy of reduced models validated against full-order simulations.

Good agreement with experimental data demonstrating practical applicability.

Abstract

This paper presents a novel derivation of the direct parametrisation method for invariant manifolds able to build simulation-free reduced-order models for nonlinear piezoelectric structures, with a particular emphasis on applications to Micro-Electro-Mechanical-Systems. The constitutive model adopted accounts for the hysteretic and electrostrictive response of the piezoelectric material by resorting to the Landau-Devonshire theory of ferroelectrics. Results are validated with full-order simulations operated with a harmonic balance finite element method to highlight the reliability of the proposed reduction procedure. Numerical results show a remarkable gain in terms of computing time as a result of the dimensionality reduction process over low dimensional invariant sets. Results are also compared with experimental data to highlight the remarkable benefits of the proposed model order reduction technique.