Analysis of Internal Resonance of a 3DOF Dynamic System Reduced from the Tower-Cable-Beam Structure

Abstract To study the complex mechanism of the high-dimensional nonlinear cable systems, a 3 degree-of-freedom model reduced from the tower-cable-beam structure is proposed and investigated in this paper. Based on the D’Alembert Principle, the dynamic equations of in-plane and out-of-plane vibration are established and simulated by the 4th-order Runge-Kutta method. The results exhibit the phenomenon of coupling internal resonance under the systematical conditions revealed by the analytical analysis on the dynamic equations. The smaller mass ratio of the cable-beam would lead to a greater vibration intensity while the tensile stiffness and initial force of the cable have no significant effect. The in-plane and out-plane cable vibrations are independent, and the internal resonance would not be excited by the harmonic excitation in the cable axis. Additionally, applying damping on any component of the system is verified to be an effective approach to vibration reduction. Compared with ordinary cables, cables with less-weight and high-strength materials would be exited to less vibration intensity under the same external excitation.