Nonlinear Normal Modes in Finite Element Model Validation of Geometrically Nonlinear Flat and Curved Beams

Abstract

Model Validation is an important step in the design of structures operating under dynamic loading. The natural frequencies and mode shapes associated with linear normal modes (LNMs) have been traditionally used to validate and update finite element models, but their usefulness breaks down when a structure operates in a nonlinear response regime. The concept of nonlinear normal modes (NNMs) has been presented as a capable extension of LNMs into nonlinear response regimes. In this work, linear model updating is performed on one flat and one curved beam using the experimentally measured natural frequencies and mode shapes coupled with gradient based optimization. Throughout the updating process, the first NNM of these structures are numerically calculated and compared with the experimentally measured NNM. This comparison is used for model validation throughout each step of the updating procedure. Results show the importance of the definition of initial geometry and effect of the large variation in boundary conditions contributing to changes in the nonlinear behavior of the model.