Dynamic Analysis of Moving Cables with Variable Tension and Variable Speed

Dynamic Analysis of an axially moving cable with time dependent tension and velocity isstudied in this paper. Tension force and the moving speed are assumed to be harmonic.It is found that there exists a specific value of speed in which natural frequency of the system approacheszero. This specific speed for such a critical condition is called critical speed and it will be proved thatincreasing the cable tension increases critical speed of the moving cable. Multiple-Scales perturbationtechnique is used to discretize the nonlinear equations of motions. Critical speeds are then obtained inwhich vibrations of motion become unstable. Stability analysis is carried out for different sets ofexcitation frequency. Dynamic responses of the system are calculated using Galerkin’s method. Acomprehensive parametric study is carried out and effects of different parameters like the moving speedand tension force on the responses are studied both in frequency and time domain