Nonlinear Reduced Order Modeling of a Curved Axi-Symmetric Perforated Plate: Comparison with Experiments

Abstract

Structures undergoing large amplitude deformations usually include nonlinear strain–displacement relationships defining a geometric nonlinearity. This type of nonlinearity can be observed in structures with fixed boundary conditions where mid-plane stretching occurs at large deflections. When considering the dynamic response of the structure under these circumstances, the once uncoupled linear normal modes become coupled at large response amplitudes changing the characteristic deformation shape as the fundamental frequency of vibration changes. Therefore, the development of nonlinear reduced order models to predict the dynamic response of such structures should account for any potential coupling between the linear normal modes. In this context, a structures’ nonlinear normal modes provide a compact characterization of modal coupling in the structural response in nonlinear regimes. This work uses experimentally measured and numerically calculated nonlinear normal modes for a curved axi-symmetric perforated plate to build a nonlinear reduced order model and gain insight to the underlying modal coupling. A comparison is made between two models and corresponding experimental structures to assess the model’s ability to describe the modal coupling.