Complex nonlinear dynamic phenomena will occur when the suspended cable is subjected to multiple parametric excitations. In order to study the effects of parametric excitation under different phases on the harmonic response of suspended cable, the model of suspended cable with parametric excitation at both ends is established, and the infinitedimensional discrete equations of motion are obtained. The subharmonic resonance in plane is studied by using the multiple scales method verified by numerical integration. The general expressions of equivalent excitation amplitude and response phase of multiexcitation system is given, and the effects of different combinations of inplane two excitations on the response amplitude and phase are qualitatively analyzed. The results show that the effect of multipoint excitations phase difference on the suspended cable response amplitude varies with 2π as a periodic variation and is symmetric about π. These excitations make the response phase of the system shift based on the response phase of the suspended cable. When the phase difference excitation between them gradually changes from 0 to π, the phasefrequency curves also shift by π. The excitation phase difference does not change the soft and hard properties of the system, but affects the response amplitude and the width of the resonance region, and the width of the resonance region is symmetrical about σ=0.
李聪,孙测世,赵碧航.端部激励相位差对悬索亚谐波共振响应的影响[J].动力学与控制学报,2023,21(4):67~75; Li Cong, Sun Ceshi, Zhao Bihang. Influence of end excitation phase difference on subharmonic resonant of suspended cable[J]. Journal of Dynamics and Control,2023,21(4):67-75.