Lateral response and energetics of cable-guided hoisting system with time-varying length

The lateral response, energetics and stability of the cable-guided hoisting system that differs from the rail-guided, such as elevator systems, is investigated in this paper. While the equations of motion are established by Hamilton's principle, the boundary conditions are obtained to calculate the natural frequencies with the modified velocity of wave propagation. Then, the governing equation is transformed into a set of ordinary differential equations through the Galerkin method and the rate of change in the energy is derived from the control volume viewpoint. The system frequencies, response of each order and energy characteristics are analyzed. The results show that the system frequencies first decrease, and then increase with the increase of the length and demonstrate that the modified velocity of wave propagation is reasonable by comparison of three approaches. The presented method proves to be effective to obtain the response of each order. According to Lyapunov’s second method, the rate of change in the energy indicates the cable-guided hoisting system experiences stability and instability during downward and upward movements, respectively.