Iterative solution of the dynamic responses of locally nonlinear structures with drift

Considering the operating point drift in the dynamic responses of locally nonlinear structures, a new iterative method based on describing functions is introduced to solve for the steady-state frequency response. Drift in the operating point arises in the presence of asymmetric nonlinearity, pre-deformation or static loads. In this study, the internal nonlinear forces are expressed using describing functions. The complex equations governing the responses of multiple frequency components are established and are iteratively solved using the Inverse Matrix Update Method. The nonlinear frequency responses can thus be rapidly obtained, and the validity of the method is verified by simulations. The presented method can be applied to large-scale structures with multiple nonlinear elements.