Prediction of higher-order harmonics generation due to contact stiffness hysteresis using Harmonic Balance: theory and experimental validation

Abstract

In the presented paper, an analytical approach based on the Harmonic Balance method is used to evaluate amplitudes of higher-order harmonics generated due to the interaction of a propagating shear wave with surfaces in frictional contact. The motion between surfaces is initially assumed to be of symmetric hysteretic stick-and-slip type. Experimental investigation is performed on steel samples with prepared contact surfaces, in order to validate the introduced solution approach. It shows that the hysteretic behavior obtained from the experiment exhibits asymmetric characteristic features. Consequently, a new asymmetric description of the hysteretic stress-strain relation is developed and used to confirm these findings. As a result, both qualitative and quantitative agreement between considered investigation methods are achieved. Finally, the identification study shows the impact of higher-order harmonics on particular features of the stiffness hysteresis.

Structural damage detection based on nonlinear vibro-acoustic modulations observed in shear horizontal wave propagation

“…nonlinear resonant ultrasound spectroscopy), sub-and higher harmonic generation [3], frequency mixing [4], modulation transfer (Luxembourg-Gorky effect) [5] and many others [6] are sensitive enough to observe any changes in structural integrity. As in the case of the whole monitoring system, the structure itself can exhibit multiple nonlinear sources, such as the material nonlinearity (usually exhibited through plasticity changes or thermal aging) [7], the cumulative presence of pores in freshly manufactured materials [8], delamination, de-bonding among the layers of the structure [8], the adhesive layer or debonding between the structure and transducer [9], and finally, the nonlinear movement of the cracks surfaces (breathing [10], micro-slip [11] or stick-and-slip [12]). All of these phenomena will have a respective influence on the recorded nonlinear responses of the structural system.…”