Nonlinear modal testing of damped structures: Velocity feedback vs. phase resonance

Abstract: In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties (modal frequency, damping ratio and deflection shape) for strongly nonlinear systems. To isolate a nonlinear mode, the negative viscous damping term of the extended periodic motion concept is approximated by ensuring phase resonance between excitation and response. In this work, an alternative approach to isolate a nonlinear mode is developed and analyzed: velocity feedback. The accuracy of the extracted modal properties and robustness of velocity feedback is first assessed by means of simulated experiments. The two approaches phase resonance and velocity feedback are then compared in terms of accuracy and experimental implementation effort. To this end, both approaches are applied to an experimental specimen, which is a cantilevered beam influenced by a strong dry friction nonlinearity. In this work, the discussion is limited to single-point excitation. It is shown that a robust implementation of velocity feedback requires the measurement of several response signals, distributed over the structure. An advantage of velocity feedback is that no controller is needed. The accuracy of the modal properties can, however, suffer from imperfections of the excitation mechanism such as a phase lag due to exciter-structure interactions or gyroscopic forces due to single-point excitation.