Effect of nonlinear impact damping on the frequency response of a torsional system with clearance

In this article we examine a particular nonlinear impact damping model that has been well accepted by the scientific community. First, we consider the damping element with a linear spring and examine the nonlinear frequency response characteristics of a torsional system. Second, the impact damping is examined along with the clearance nonlinearity including the backlash problem. Three semi-analytical methods, namely the Describing Function Method, Multi-term Harmonic Balance Method and Stochastic Linearization Method, are utilized to investigate the effect of impact damping. Feasibility of such methods is confirmed by comparing predictions with results yielded by a numerical method. The differences between impact damping and linear viscous damping mechanism are studied in terms of frequency responses, time histories, and the minimum number of harmonics required to simulate the behavior given sinusoidal excitations. Furthermore, the effect of impact damping on sub- and super-harmonic responses and quasi-periodic regimes are examined.