Nonlinear Vibration Caused by Beam of Cable Structures

Abstract

The nonlinear vibrations of cables excited by the vibration of beam were investigated. At first, a simple connection condition and boundary condition of the cable-stayed beam structure were applied. The nonlinear equations of motion of the cable-stayed beam structure were derived, and the static sag of the cable as well as the geometric nonlinearity was considered, moreover, Appling the multi-scale perturbation method, the nonlinear vibrations of cables were studied, the nonlinear vibration response of cables was analyzed by the Runge-Kutta numerical method to obtain the frequency-response curves. The results indicate that the beam small scale vibration can stimulate the cable the large scale movement when local oscillation frequency of beams is in the certain region, it affects the cable-stayed beam structure the stability and the security in the Engineering. For the system in which the damping and the frequency ratio was given, the enough low excitation amplitudes can avoid the system resonances.