索结构-弹性支座耦合系统的多尺度建模理论与动力学研究

Cable’s elastic supports, such as long-span bridge deck、high-rise bridge tower and transmission-line tower, increase fast due to more and more long-span suspended-cable bridges, stay-cable bridges and cross-ocean high-power transmission lines. Different from ideal rigid supports, strong dynamic interaction between cables and elastic supports occurs. With a small ratio of cable’s mass(or rigidity) to support’s and with cable’s geometry nonlinearity, cable-elastic support would be a nonlinear dynamic coupled system with multiple time scales. This project would aim at a systematic investigation into multiscale modeling and dynamic analysis for cable-elastic support coupled system: Taking cable-mass and cable-cantilever beam as two basic models, and transforming the cable-support coupled moving boundary conditions into high-order boundary modulation terms by order analysis and multiple scale expansion, we would establish a general theory for multiscale modeling of cable-support coupled systems through constructing solvability conditions, i.e., boundary modulation approach; based upon linear modal analysis for the multiscale models, quantitative and qualitative relations between coupled modes and dynamic interaction would be constructed; applying primary/secondary resonant excitations, this project would find cable-support’s coupled dynamic responses, and conduct full investigations into their stability and bifurcation characteristics. This project’s results would enhance theoretical study of modeling structure’s dynamic interaction, and lay the theoretical foundations for engineering cable-elastic support system’s dynamic design.

随着大跨度悬索桥、斜拉桥、跨海输电线的出现，大跨度桥面、高耸桥塔、高耸输电塔架等弹性支座结构不断增多。区别于理想刚性支座，弹性支座将与索结构发生强烈的动力耦合作用；索与支座的质量比/刚度比是小参数，同时考虑索的几何非线性，则索-支座系统将是一个非线性多时间尺度耦合动力学系统。本项目拟针对索结构-弹性支座开展系统的多尺度耦合建模理论与动力学研究：以索-质量块和索-梁为基本模型，利用量阶分析和多尺度展开，将耦合动边界转化为高阶边界调制项，通过构造可解条件建立索-支座系统多尺度耦合建模的一般理论，即边界调制方法；基于多尺度耦合模型的模态分析，揭示索-支座系统耦合模态与动力耦合强度的定量/定性关系；针对主/次共振外激励，分析求解索-支座耦合系统的稳态动力响应，深入考察其稳定性与分岔特性。该项目的研究成果将推进结构耦合动力学的理论建模研究，为大跨度工程索结构-弹性支座耦合系统的动力设计奠定理论基础。