An approach of dynamic response analysis of nonlinear structures based on least square Volterra kernel function identification

Analysis of the dynamic response of a complex nonlinear system is always a difficult problem. By using Volterra functional series to describe a nonlinear system, its response analysis can be similar to using Fourier/Laplace transform and linear transfer function method to analyze a linear system's response. In this paper, a dynamic response analysis method for nonlinear systems based on Volterra series is developed. Firstly, the recursive formula of the least square method is established to solve the Volterra kernel function vector, and the corresponding MATLAB program is compiled. Then, the Volterra kernel vector corresponding to the nonlinear response of a structure under seismic excitation is identified, and the accuracy and applicability of using the kernel vector to predict the response of a nonlinear structure are analyzed. The results show that the Volterra kernel function identified by the derived recursive formula can accurately describe the nonlinear response characteristics of a structure under an excitation. For a general nonlinear system, the first three order Volterra kernel function can relatively accurately express its nonlinear response characteristics. In addition, the obtained Volterra kernel function can be used to accurately predict the nonlinear response of a structure under the similar type of dynamic load.