Dynamics of piezoelectric structures with geometric nonlinearities: A non-intrusive reduced order modelling strategy

A reduced-order modelling to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities is proposed in this paper. A formulation of three-dimensional finite element models with global electric variables per piezoelectric patch, and suitable with any commercial finite element code equipped with geometrically nonlinear and piezoelectric capabilities, is proposed. A modal expansion leads to a reduced model where both nonlinear and electromechanical coupling effects are governed by modal coefficients, identified thanks to a non-intrusive procedure relying on the static application of prescribed displacements. Numerical simulations can be efficiently performed on the reduced modal model, thus defining a convenient procedure to study accurately the nonlinear dynamics of any piezoelectric structure. A particular focus is made on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity. Reference results are provided in terms of coefficients of the reduced-order model as well as of dynamic responses, computed for different test cases including realistic structures. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a reduced-order modeling method to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities, which can efficiently perform numerical simulations and provide a convenient procedure for studying nonlinear dynamics. The focus is on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity, with reference results provided for different test cases involving realistic structures.