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

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. • Model order reduction for structures with geometric and piezoelectric nonlinearity. • Direct computation of the invariant manifold from finite element problem. • Efficient technique accounting for electrostrictive response of the piezoelectric. • High accuracy of the results compared to full-order simulation. • Application to micro-electro mechanical systems with complex geometry. [ABSTRACT FROM AUTHOR]