Identifying parameters of nonlinear structural dynamic systems using linear time-periodic approximations

Abstract

While numerous mature parametric identification methods are available for linear systems, there are only a few methods capable of identifying parametric models for multiple degree of freedom nonlinear systems. In a previous work, the authors proposed a new identification routine for nonlinear systems based on harmonically forcing a system in a periodic orbit and then recording deviations from that orbit. Under mild assumptions one can model the response about the periodic orbit using a linear time-periodic system model that is relatively easy to identify from the measurements using a variety of techniques. The method provides an estimate of the time periodic state coefficient matrix of the system which gives direct information on the order of the system and the nonlinear-parameters. A prior work explored the method in detail for a single degree-offreedom system, but it has only been applied to an MDOF system with a limited set of excitation conditions. This work explores a range of possible excitation signals using an analytical model of a cantilever beam with a cubic spring at its tip. Numerical continuation techniques are used to find the stable and unstable periodic responses of the beam and different excitation strategies are explored. Additionally, the method is validated on the analytical model with a conventional approach for nonlinear system identification. The most promising strategies are then applied to a real beam with a significant geometric nonlinearity.