Forced Torsional Vibration of a Two Degrees of Freedom System with a Clearance : 2nd Report, Analytical Solution

An analytical solution of the forced tortional vibration of a two degrees of freedom system with a clearance between two rotating bodies is derived. The analytical solution is obtained by connecting the solutions for the motion of each body caused by successive collisions of the bodies, without making assumptions on the number of times of collisions that occur during a cycle of the forced motion and on the periodicity of the collisions. The analytical solution shows the existence of a phenomenon of multi-time collisions at one side of the clearance during a half cycle of the forced motion. Effects of the dimension of the clearance and the average angular velocity on the strength of the impact force are investigated. The results of the analytical solution show good quantitative agreements with those of the simulation.