Modeling and Parametric Analysis of In-Plane Free Vibration of a Floating Cable-Stayed Bridge with Transfer Matrix Method

Abstract

As a classic bridge type, cable-stayed bridge is widely used because of its superior spanning capacity. Based on the mechanical characteristics of stay cable supporting deck, we propose a novel mechanical model aiming to evaluate the vertical bending stiffness of a floating cable-stayed bridge, namely, multi-beam model with discrete springs. First, a single-tower cable-stayed bridge is modeled as a triple-beam model with discrete springs in order to introduce the novel method easily. In this model, the stay cables are simplified as springs without mass and the single tower is regarded as an Euler–Bernoulli beam with consideration of the effect of axial force. At the same time, the bridge deck has been cut into two Euler–Bernoulli beams at the intersection of a deck and a tower. Then equations governing vibrations of the beam and tower are derived according to Hamilton’s principle for dynamic problems in elastic body under equilibrium state. The program is established by transfer matrix method to solve the eigenvalues of the system along with its boundary and matching conditions. Thus, the vertical bending stiffness of the floating cable-stayed bridge can be evaluated based on the frequency. In addition, the influences of the cables’ material, location, stiffness and number on vertical bending stiffness are analyzed in detail when the steel cables are replaced with CFRP cables. Lastly, the same method is directly extended to modeling the floating multi-tower cable-stayed bridge. The results, which are validated by commercial finite element software, demonstrate that the proposed mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.