Nonlinear vibration analysis of mechanical systems with multiple joint clearances using the method of multiple scales

In this paper, the method of multiple scales is used in an innovative way to conduct a vibration analysis of a mechanical system such as a sliding pendulum with multiple clearances. Analytical approaches can give more insight into such problems due to the nonlinearity involved. At first, it is assumed that a single clearance exists in the joint between the slider and the guide. Then, a second clearance is assumed in the joint position between the pendulum and the slider. The horizontal vibration of the system is ignored. For the first case, the clearance is modeled just as a nonlinear spring and in the second one a nonlinear damper is also considered which gives a more realistic model. The Lankarani-Nikravesh contact force model is used to represent the contact force between joined bodies. Primary resonance and internal resonance are discussed in detail. It is shown that the pendulum angle is not so affected by the clearance. The natural frequency corresponding to the oscillation of the pendulum is far from the one corresponding to the vertical motion of the system. However, the vertical motion of the system components can have influence on each other.