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. One of the goals of this area is to obtain a model that accurately predicts the dynamics of the system. However, the nonlinear eff ects caused by large displacements and boundary conditions like gap, backlash or joint 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. Time-domain data experimentally measured are used to identify the Volterra kernels, which are expanded with orthogonal Kautz functions to facilitate the identification process. The nonlinear parameters are then estimated through a model updating process involving optimization of the residue between the numerical and experimental kernels. The advantages and drawbacks of the Volterra series for modeling the behavior of nonlinear structures are finally indicated with suggestions to overcome the disadvantages found during the tests.