A nonlinear reduced order model with parametrized shape defects

We propose a formulation to derive a reduced order model for geometric nonlinearities which is shown to be valid for a set of parametrized defects. The latter are imposed in terms of the superposition of precomputed perturbations of the nominal structure's 3D-mesh, and parametrized by their amplitudes. A reduced order model is then built once and for all using these defect shapes and the nominal model information only. A suitable reduced order basis is introduced as well in order to effectively represent the influence of the defects on the dynamics of the structure. In contrast to many nonlinear parametric reduced order models, the one we propose does not need any previous training of the model in the parameter space. In this way, prohibitively expensive full order simulations can be avoided and offline times are greatly reduced. Numerical tests are performed on a MEMS resonator and a silicon micro-beam to study the effect of shape imperfections on the dynamic response of the system.