Analysis of Nonlinear Torsional Dynamics Using Second-Order Solutions

Based on the modal series method, this paper derives the second- and first-order solutions of torques for investigating nonlinear torsional dynamics. The derivatives of the two types of solutions are compared to explain the advantage of the second-order solutions. The index is given for evaluating the feasibility of solutions. Subsequently, several nonlinearity indices are defined to quantify the effects of nonlinear modal interactions on torsional dynamics, and the suitable indices are determined for analyzing nonlinear torsional dynamics. The systematic method is developed for the analysis of nonlinear torsional dynamics. Furthermore, the concept of nonlinear modal interactions is extended to deal with both the fundamental and the combination modes; the nonlinearity contribution factors are emphasized. The study is implemented on two modified cases from the IEEE first benchmark model, which validates the presented method for investigating torsional dynamics in the stressed case and gives new engineering insights into nonlinear torsional dynamics.