Study on longitudinal vibration of friction hoist skips based on Ritz series

For a friction hoist, the skip vibration deserve thorough study to solve kinds of relevant problems, which include when to monitor and what frequency band to scan the hoist actual load. Based on the Power Balance principle, Ritz series method has the particular advantage that provides standard discrete differential equations for the vibration of continuous elastic pole. In this study, a dynamic model was built according to the straight pole vibration theories. While applied on the skip vibration just after loading, Ritz series benefits the problem solution and conclusion drawing about vibration factors greatly. Simulations based on differential equations in MATLAB shows head ropes´ length and the skip total mass affect both shock time and vibration frequency at every order, while the damping only brings change for attenuation rate.