Modal resonant dynamics of cables with a flexible support: A modulated diffraction problem. (June 2018)

• Record Type: Journal Article
• Authors: Guo, Tieding; Kang, Houjun; Wang, Lianhua; Liu, Qijian; Zhao, Yueyu
• Is Part Of: Mechanical systems and signal processing. Volume 106(2018)
• Page Start: 229
• Page End: 248
• Publication Date: 2018-06
• Subjects: Flexible supports -- Cable-support coupling -- Asymptotic approximation -- Mode interaction; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2017.12.023
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: General cable-support coupled dynamics is categorized into two distinct kinds, i.e., diffraction dominated dynamics (with the cable excited) and radiation dominated dynamics (with the support excited). Cable's two-to-one mode interaction with a flexible support is formulated as a modulated diffraction problem. Using multi-scale expansions and asymptotic approximations, a reduced model for the modulated diffraction problem is derived. Flexible support induced modulation effects are investigated asymptotically, by constructing nonlinear coupled frequency/force response diagrams. Abstract: Modal resonant dynamics of cables with a flexible support is defined as a modulated (wave) diffraction problem, and investigated by asymptotic expansions of the cable-support coupled system. The support-cable mass ratio, which is usually very large, turns out to be the key parameter for characterizing cable-support dynamic interactions. By treating the mass ratio's inverse as a small perturbation parameter and scaling the cable tension properly, both cable's modal resonant dynamics and the flexible support dynamics are asymptotically reduced by using multiple scale expansions, leading finally to a reduced cable-support coupled model (i.e., on a slow time scale). After numerical validations of the reduced coupled model, cable-support coupled responses and the flexible support induced coupling effects on the cable, are both fully investigated, based upon the reduced model. More explicitly, the dynamic effects on the cable's nonlinear frequency and force responses, caused by the support-cable mass ratio, the resonant detuning parameter and the support damping, are carefully evaluated.