Vector form intrinsic finite element based simulation on parametric vibration of cables

The parametric vibration is mainly caused by the vibration of the end supports connecting the cables. The cable is the main force component of the cable-stayed bridge. A small disturbance of the stayed cable will be motivated to oscillate with large amplitude once the natural frequency of cables meets a certain multiple relationship with that of support motion，which will cause security problems of bridges. As the complexity of nonlinear problems in the parametric vibration，the traditional analytical methods are unsuitable to be applied in engineering. Hence，the vibration analysis of the stayed cable under dynamic boundary conditions were conducted based on the Vector Form Intrinsic Finite Element method（VFIFE）in this paper and the accuracy of the results were validated by comparison with numerical solution of the governing equations. In addition，the characteristics of the main resonance regions and the main parameter resonance regions excited by axial support motion were discussed. The effects of the angle of inclination，damping ratio and the wind loads on parametric vibration were also analyzed，respectively. The results showed that the VFIFE method is enable to efficiently simulate the parametric vibration of cables under various conditions，which is benefit to engineering application. © 2023 Nanjing University of Aeronautics an Astronautics. All rights reserved.