On the Dynamic Response of a Two-Degree-of-Freedom System With Dry Friction and Elastic Stop

The contact interface is one of the essential components of structural systems, introducing friction and non-smooth constraints, which will cause nonlinear dynamic behavior. This survey provides an insight into the dynamic response of a simplified model with two moving parts in detail. The proposed model can be applied to analyze the dynamic behavior of a rotor system with pedestal looseness fault. First, a two-degree-of-freedom system is established, and the nonlinear force caused by friction and elastic stop is introduced between the two moving parts. Dimensionless governing equations are derived, and the harmonic balance method and the shooting method are used to obtain the periodic solution. Floquet theory and Poincaré mapping are applied to analyze stability. The amplitude-frequency curves obtained by the two methods are compared considering friction merely, and the accuracy of the harmonic balance method is verified by the numerical integration method. Then, the features of energy dissipation versus excitation frequency are present, and influences of friction force amplitudes on the dynamic response are studied. The periodic solution is unstable considering friction and elastic stop in some excitation frequency ranges, and Hopf bifurcations exist correspondingly, indicating quasi-periodic motion occurs. The frequency domain of periodic motion contains super-harmonic components merely, while the frequency domain of quasi-periodic signal is composed of combined frequencies. Since Hopf bifurcation indicates a new periodic solution whose frequency is incommensurable with the original one, a formula for explaining combined frequencies is presented. Meanwhile, there are multiple collisions phenomena per cycle in time history. Finally, the influences of parameters on the dynamic response are studied. Note that the model in this survey may be regarded as a single-degree-of-freedom system with a friction-impact damper, which is beneficial to design nonlinear vibration absorbers based on friction and impact for vibration suppression.