A phase resonance approach for modal testing of structures with nonlinear dissipation

The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is still in its infancy. The purpose of this work is to overcome its present limitation to conservative nonlinearities. Our approach relies on the recently extended periodic motion concept, according to which nonlinear modes of damped systems are defined as family of periodic motions induced by an appropriate artificial excitation that compensates the natural dissipation. The particularly simple experimental implementation with only a single-point, single-frequency, phase resonant forcing is analyzed in detail. The method permits the experimental extraction of natural frequencies, modal damping ratios and deflection shapes (including harmonics), for each mode of interest, as function of the vibration level. The accuracy, robustness and current limitations of the method are first demonstrated numerically. The method is then verified experimentally for a friction-damped system. Moreover, a self-contained measure for estimating the quality of the extracted modal properties is investigated. The primary advantages over alternative vibration testing methods are noise robustness, broad applicability and short measurement duration. The central limitation of the identified modal quantities is that they only characterize the system in the regime near isolated resonances.