Modeling, dynamics, and parametric studies of a multi-cable-stayed beam model
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O R I G I NA L PA P E R
Yunyue Cong
· Houjun Kang · Guirong Yan · Tieding Guo
Modeling, dynamics, and parametric studies of a multi-cable-stayed beam model
Received: 7 May 2020 / Revised: 26 July 2020 / Accepted: 13 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract To study the dynamic behavior of cable-stayed bridges, a linear multi-cable-stayed beam model is developed to investigate its in-plane and out-of-plane transverse vibrations. From the full-bridge perspective, an in-plane nonlinear single-mode discrete model is established. First, the in-plane and out-of-plane motion equations of the system and their boundary conditions are derived. Second, by employing the separation of variables method, the linear eigenvalue problems are solved. The influences of the mass ratio, stiffness ratio, and cable sag on the occurrence of global, local, and coupled vibration modes are studied. Third, frequency response, amplitude response, phase diagram, time history, and power spectrum are extracted to investigate the system’s nonlinear dynamic behaviors. The obtained results demonstrate that for the in-plane motion, the occurrence of global and local modes of the system depends on the mass and stiffness ratios between cable and beam significantly; for the out-of-plane motion, without the elastic support of the cable, the global modes occur, which can be suppressed by adjusting the mass and stiffness ratios between cable and beam but may in turn induce the cable’s local vibration modes; for the nonlinear analysis, the single-degree-of-freedom system behaves like a hardening spring. Its lower branch behaves more complicated than the higher one and has a double-periodic steady-state solution. The system with large damping ratio behaves shows weak hardening spring property.
1 Introduction Among the infrastructure systems, cable-stayed bridges have been popular due to their large spanning capacity, rational mechanical properties, reasonable cost, and mature construction technologies. In the past several decades, the main span has been continuously increasing and currently the span has reached more than one kilometer. The larger span bridges bring new challenges for design and construction. Due to the long spanning of cable-stayed bridges, their dynamic behaviors become more complicated and more sensitive to small disturbances due to coupling interactions, making structural analysis more complicated. Therefore, it is imperative to extensively investigate the dynamic behaviors and coupling properties from different perspectives. Thus far, researchers have carried out a lot of work on the family of cable-beam models, consisting of a cable and a beam with different type of excitations, in order to explore their interaction mechanism. In 1993, Fujino et al. [1] first proposed a 3-DOF analytical model of a cable-stayed beam based on the local–global mode approach and studied the auto-parametric resonance of the model under harmonic excitation experimentally and Y. Cong · H. Kang (B) · T. Guo College
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