Planar nonlinear dynamic behavior of a cable-stayed bridge under excitation of tower motion

• Published in: European journal of mechanics, A, Solids Vol. 76; pp. 91 - 107
• Main Authors: Cong, Yunyue, Kang, Houjun
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.07.2019; Elsevier BV
• Subjects: Arch bridges; Bridge towers; Cable-stayed bridges; Cable-stayed model; Cables; Dynamical systems; Galerkin method; Harmonic excitation; Multiscale analysis; Nonlinear analysis; Nonlinear dynamics; Ordinary differential equations; Partial differential equations; Perturbation methods; Primary resonance; Subharmonic resonance; Support motion; Nonlinear dynamics; Primary resonance; Cable-stayed model; Support motion; Subharmonic resonance
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2019.03.010

Based on a double cable-stayed shallow arch model of the cable-stayed bridge, the novel dynamic theory and analysis of nonlinear dynamic behavior of the system when cables' upper ends are subjected to harmonic excitation introduced by motion of tower are established and carried out. A set of partial differential equations governing the motion of present system are derived firstly according to the classic dynamic theories of cables and the shallow arch. Then, they are used to obtain the ordinary differential equations of the system by Galerkin's integral method. The corresponding modulation equations are derived by implementing the standard process of perturbation method of multiple scales when the 1:1:1 internal resonance among the lowest modes of cables and the shallow arch and external resonance of the system occur simultaneously. Frequency- and force-response curves are plotted to explore the rich dynamic behaviors of the system. The research shows the asymmetric harmonic excitations can cause the different jump phenomenon of cables, even the reverse jump is observed when the subharmonic resonance occurs. •Propose planar dynamic theory of a cable-stayed bridge considering tower motion.•Establish the modulation equations of the system under primary resonance.•Establish the modulation equations of the system under subharmonic resonance.•Observe many interesting nonlinear dynamic phenomena of the system.•Reveal some mechanism of large vibration of cables.