An Equivalent Identification Method for Dynamic Loads Acting on Nonlinear Structures

An efficient dynamic load identification method for nonlinear structures is proposed. Assuming that the nonlinear elements of a structure can be separated, or the structural kinetic equation can be available, the whole structural damping and stiffness matrices can be divided into linear and nonlinear sub matrices. Regarding the effects of the nonlinear elements on the linear ones as dynamic load constraints, which can be realized by moving the product of the nonlinear sub matrices and their corresponding responses to the right-hand side of the original kinetic equation, a remaining linear structure subjected to multi-source of dynamic loads can then be obtained. The instability of the obtained structure caused by the load equivalence is discussed and improved. The case that the characteristics of the nonlinear parameters are unknown is also investigated. Finally, based on the improved structure, Green’s kernel function method, LSQR regularization is employed to reconstruct the dynamic loads. The effectiveness of the proposed method is proved by two numerical examples and an engineering application.