Linearization of modal parameters in Duffing oscillator using the random decrement technique

In this study, it is investigated how the random decrement (RD) technique can be used to linearize the nonlinear stiffness of a single degree of freedom system with a hardening spring, known as a Duffing oscillator. The linearization is implemented by using a set of trigger levels in the response signal to define RD signatures. The modal parameters are estimated at the same response level for various excitation force levels, from the RD signatures describing the system at that specific level, and extracting the modal parameters using time domain parameter extraction methods. The system described by the RD signature is assumed to behave as a linear system with an equivalent stiffness depending on the trigger level. Various triggering conditions for the RD technique are investigated, to study their applicability in linearizing the nonlinear system. The results of the study show that, with the Local Extremum, and Envelope triggering condition, the RD technique can be successfully used to linearize the modal parameters of the Duffing oscillator.