Identification of nonlinear joints using amplitude-dependent modal parameters with high-accuracy reduction techniques

Abstract

An efficient identification method using amplitude-dependent modal parameters is developed for systems with nonlinear joints. In this method, the nonlinear modal parameters of lightly damped systems are calculated by the extension of the periodic motion concept (EPMC). First, an exact reduction technique is applied to reduce computational effort due to the sparsity of the nonlinear force. Next, the frequency response function (FRF) matrix of the linear part is approximated using the incremental modal expansion, achieving high accuracy to speed up the solution process. An approach to identifying the parameters of the joint model is then introduced, which utilizes the EPMC and the reduction techniques. The objective function for minimization is calculated as a function of the errors between the calculated and measured nonlinear modal parameters, and the corresponding sensitivity matrix is derived. In this work, the modal motion amplitude of a certain reference degree of freedom (DOF) is used as a reference quantity to match the calculated and measured data in the identification process. The efficiency and convergence of the identification method are validated through both simulated and experimental case studies. Results indicate that the identification method can be successfully applied to practical assembly structures.