A Combined Numerical-Experimental Approach for the Damping Evaluation of Non-Linear Dissipative Vibration Systems

Many nonlinear systems exhibit phenomena that have no counterpart in linear theory, like energy dependent modal parameters, sudden amplitude changes due to bifurcations or harmonic coupling between modes. Well established methods for the experimental analysis of linear systems, where the system is simply excited in open-loop, can not cope with such nonlinear effects. However, a novel approach called experimental continuation, allows to account for strongly nonlinear behavior by tracing the solution curves of nonlinear systems through fold bifurcations experimentally. Within the Priority Program Calm, Smooth and Smart (SPP1897) continuation has been exploited for the numerical computation of nonlinear normal modes applying the harmonic balance method [9, 10]. The experience gained in the first phase was consequently used by embedding a continuation algorithm in a closed-loop experiment utilizing a real-time processor. Herein, the control-loop is designed to stabilize unstable steady states of the system under harmonic excitation. This enables the experimental evaluation of nonlinear frequency response curves together with the resonance frequency-and nonlinear damping-curves.