Reduced Order Modelling Of Electro-Mechanical Microsystems Through Invariant Manifolds
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This paper presents the first application of the direct parametrization method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field. The formulation proposed is intended for model order reduction of electrostatically actuated resonating Micro Electro Mechanical Systems. To fit the coupled problem in the recently developed numerical frameworks of the parameterization method, a new mixed fully Lagrangian formulation is first proposed which contains only explicit polynomial nonlinearities and intended for a discretization in the framework of finite element procedures. Finally, a validation is performed on the classical parallel plate configuration between different reduced-order-models and also against full-order simulations operated with a time integration approach. Numerical results show a remarkable performance both in terms of accuracy and wealth of nonlinear effects that can be accounted for, including transitions of the frequency response curves from hardening to softening, superharmonic, subharmonic or parametric resonances
