Dynamic modeling and linear vibration characteristic of cable- stayed bridges. Part II: Eigenvalue and hybrid method

In Part I of this study, the dynamic model of cable-stayed bridges has been developed by the Hamilton's principle, and the linearization procedure is firstly performed to obtain the equations of motion governing the linear free response of cable-stayed bridges, which are applied to perform the eigenvalue analysis of the cable-stayed bridge in Part II. To achieve this, the separation-of-variable method is firstly introduced to the separation solutions of in-plane and out-of-plane problems of cable-stayed bridges. Then, the hybrid method is proposed to determine eigenvalue solutions of the linear problems based on the separation-of-variable solutions, and three types of eigenvalue of cable-stayed bridges are obtained. The correctness of the method is validated through the comparison of the numerical results with the finite element results as well as the corresponding numerical algorithm. Following, the method is applied to perform the parametric analysis of in-plane and out-of-plane problems of the cable-stayed bridge, and the effects of some design parameters on the in-plane and out-of-plane natural frequencies are systematically investigated as well as the dynamic interaction. It is shown that the frequency spectra of the cable-stayed bridge exhibit the frequency curve veering and frequency crossover phenomena, and the mode shapes of the cable-stayed bridge may exhibit the local, global and coupling characteristics.