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.

翻译：本文提出了一种直接参数化不变流形方法的新推导，能够为非线性压电结构构建无仿真降阶模型，特别侧重于微机电系统中的应用。采用的本构模型通过引用铁电体的朗道-德文希尔理论，考虑了压电材料的迟滞和电致伸缩响应。结果通过基于谐波平衡有限元法的全阶仿真进行验证，以突出所提出的降阶过程的可靠性。数值结果表明，由于在低维不变集上的降维过程，计算时间显著减少。研究结果还与实验数据进行了比较，以展示所提出的模型降阶技术的显著优势。