Nonlinear dynamics modeling and analysis of two rods connected by a joint with clearance

In this paper, the nonlinear dynamic behaviors of two elastic rods connected by a joint with clearance are investigated. The rods and joint system are modeled by two degrees of freedom of mass-spring system with a clearance. The equations of motion of the mass-spring system with clearance are established by means of d'Alembert's principle. Due to the nonlinearity caused by clearance, the dynamic properties of the system are studied using the averaging method and compared with numerical solutions. The frequency responses of the system subjected to cosinusoidal excitation are obtained as well as the effects on the vibration characteristics induced by different gap sizes are investigated. The stability condition for steady solutions is presented based on Lyapunov theory. The method for detecting the multi-value performances of the frequency response has been proposed. Based on this method, the effects of the clearance size on the multi-value response characteristics are investigated, and the critical value of the clearance is obtained.