索-塔(梁)耦合结构非线性宽频减振的渐近理论、优化与实验研究

Cable-tower(beam) systems have been extensively used in long-span bridges and power transmission structures, and passive controls like tuned mass dampers (TMD) are important for their vibration suppressions. However, TMD’s application is restricted seriously due to its narrowband vibration absorption, and therefore it is an urgent need for the engineering community to develop broadband vibration mitigation strategies. As a research focus, vibration control based upon the nonlinear absorber or nonlinear energy sink (NES) is broadband. But the present investigations are mainly parametric optimizations for simple model systems, while main structure-nonlinear absorber’s coupled dynamics did not get enough attentions which they deserve. Recently, we have got two new basic observations: firstly, a nonlinear absorber (or NES) might excite main structure’s new complicated dynamics (e.g., strongly modulated responses) due to its strong nonlinearity, although it indeed causes vibration’s reductions; secondly, there are two key dimensionless parameters for the cable-tower(beam)-absorber coupled system, one is very large and the other is really small. Therefore, from the perspective of dynamic interactions, the present project aims to establish an asymptotic formulation for the cable-tower(beam)-absorber coupled system, develop broadband vibration suppression strategies using the asymptotically reduced cable-tower(beam) models, and propose an optimal passive control for the nonlinear absorbers based upon fundamental dynamics principles, with also experimental verifications. The results would promote the theoretical investigations for the nonlinear broadband vibration suppressions using NES, and also lay the theoretical foundations for engineering cable-tower(beam) system’s vibration mitigations.

索-塔(梁)体系广泛应用于大跨度桥梁、输电线结构，被动控制是其重要的减振措施，如调谐质量阻尼器(TMD)。但TMD受到减振频率带宽过窄的严重制约，工程界迫切需要发展宽频减振策略。作为研究热点，基于(强)非线性吸振器(NES)的减振具有宽频效应。但目前以简单模型的参数优化设计为主，缺乏针对主结构-吸振器体系的耦合动力学研究。我们新近观察到两个重要事实：一是(NES)吸振器在减振的同时，其强非线性可能激发主结构新的复杂行为(如强调制响应)；二是索-塔(梁)-吸振器体系同时包含一个大参数和小参数(无量纲)。因此，本项目拟从耦合动力学角度，建立索-塔(梁)-吸振器(NES)体系的渐近分析理论，发展基于索-塔(梁)渐近约化模型的宽频减振策略，提炼出基于动力学原理的非线性吸振器最优配置理论，并开展实验验证。研究成果将推进非线性宽频减振的理论研究，为索-塔(梁)结构减振设计奠定理论基础。

复杂索-塔/梁耦合结构广泛应用于悬索桥、斜拉桥、输电线等工程结构系统。开展复杂组合结构的耦合动力学建模、分析和减振研究是准确预测和合理设计工程索-塔/梁结构体系的关键理论基础。.本项目针对索/塔/梁及其耦合结构开展复杂动力学建模、模型降阶、渐近分析和宽频减振研究，主要内容包括三个方面：.(1) 以索/梁/塔及其组合结构为研究对象，发展耦合动力学建模与非线性模型降阶方法。.(2) 以索/梁/塔及其耦合动力学模型为基础，开展渐近分析、模态局域化、能量传输与被动减振研究。.(3) 针对索/塔/梁及其耦合结构，发展阻尼器、调谐质量阻尼器和能量阱等多种减振方案，研究主结构-吸振器耦合动力学特性。.项目完成后，研究团队取得系列成果，在国内外学术刊物发表SCI论文29篇。主要研究成果包括以下方面：.(1) 以索/梁/塔及其耦合结构为代表的复杂结构体系为对象，凝练边界调制基本概念，并在强/弱耦合情形建立耦合动力学建模方法。揭示非线性结构Galerkin截断发生错误的内在机制，发展基于低阶消除的非线性模型降阶技术。.(2) 针对以索-梁/塔为代表的组合结构，建立耦合模态与解耦部件模型之间的通用关系式。利用渐近分析和非线性模态方法，揭示耦合模态发生线性或非线性局域化的内在机制。.(3) 以索/塔/梁及其耦合结构为对象，综合理论分析、参数优化和模型实验，揭示阻尼器、线性吸振器、非线性吸振器减振效果以及主结构-吸振器耦合动力学特性。.该项目研究成果将推进复杂组合结构耦合动力学理论和结构高效宽频减振研究，为复杂索-塔/梁结构体系的动力分析和减振设计提供理论基础。