Summary
This work introduces the application of the Direct Parametrisation method for Invariant Manifolds to a fully coupled multiphysics problem involving nonlinear vibrations of deformable structures under an electrostatic field. The proposed formulation aims at model order reduction for electrostatically actuated resonating Micro-Electro-Mechanical Systems (MEMS). The continuous problem is rewritten in a novel mixed fully Lagrangian formulation with explicit polynomial nonlinearities for direct handling by the parametrisation method, which utilises automated asymptotic expansions. Validation is conducted on simple MEMS, comparing different formulations and reduced-order models to full-order simulations. The results demonstrate high accuracy and capture nonlinear effects, including the transition from hardening to softening behaviour and investigation of secondary resonances.
