Identification of mechanical systems with local nonlinearities through discrete-time Volterra series and Kautz functions

Mathematical modeling of mechanical structures is an important research area in structural dynamics. The goal is to obtain a model that accurately predicts the dynamics of the system. However, the nonlinear effects caused by large displacements and boundary conditions like gaps, backlash, joints, as well as large displacements are not as well understood as the linear counterpart. This paper identifies a non-parametric discrete-time Volterra model of a benchmark nonlinear structure consisting of a cantilever beam connected to a thin beam at its free end. The time-domain data of the modal test are used to identify the Volterra kernels. To facilitate the identification process, the kernels are expanded with orthogonal Kautz functions to decrease the number of parameters to be identified. The nonlinear parameters are also estimated by a nonlinear model updating technique involving optimization of residue of the numerical and experimental kernels. The capability of the representation of the nonlinear phenomena is investigated through numerical simulations. The paper concludes by indicating the advantages and drawbacks of the Volterra series for modeling the behavior of nonlinear structures with suggestions to overcome the disadvantages found during the tests.