Towards finite element model updating based on nonlinear normal modes

Abstract

Local nonlinearities typically occur due to large deformation in certain parts of a structure or due to the presence of nonlinear coupling elements. Often the dynamic behavior of such elements is a priori unknown and has to be investigated experimentally before they can be included in numerical calculations. In this contribution an integrated method for estimation of linear as well as nonlinear system parameters based on the nonlinear normal modes (NNMs) of the structure is proposed. The characteristics of the nonlinear and linear parts of an assembly both contribute to its NNMs. Assuming that the functional form of the nonlinearity is known or can be estimated through non-parametric identification techniques, this feature can be exploited for the purpose of model updating. For the updating process the measured and calculated NNMs of a system are compared and their difference is minimized. In this context the numerical calculation of NNMs is performed using the Harmonic Balance Method (HBM). The properties of the proposed method are demonstrated on the numerical example of a 4DOF oscillator with a cubic nonlinearity. Furthermore, the effectiveness of the method is shown by updating the FE-model of a beam with cubic nonlinearity based on experimental data.