频率空间重排下耦合系统的优化减振机制研究

The strong vibration is greatly harmful to agriculture， industry, scientific research and daily life, and brings great challenge to the performance of widely applied shock absorber. In this project, internal mechanisms of vibration suppression with an optimal spatial frequency arrangement are revealed to improve the damping effect of the shock absorber by exploring the effects of spatial frequency arrangements on vibration suppression of coupled oscillators. A space-coupled oscillator model is built based on the spatial couplings between bridge's bodies and shock absorbers. The critical coupling strength for stable steady state of the coupled system is determined based on the stability analysis method for each spatial frequency arrangement. Distribution functions of the critical coupling strengths for all possible spatial frequency arrangements are explored with theory of statistics. Moreover, a parameter related to the spatial frequency arrangements is defined to uncover the internal mechanisms and universal laws of the distribution functions by finding the relationships between the parameter and the critical coupling strength. Ultimately, an optimal frequency distribution is determined to effective vibration suppression with minimum costs. The research is beneficial to the practical guidance of vibration damping and control on the bridges, roads and buildings.

强烈振动严重危害着工农业生产、科学研究和日常生活，并对广泛采用的阻尼减振器的性能提出了很大的挑战。本项目通过探索阻尼减振器的频率空间排列对耦合振子系统减振的影响，确定最优频率空间排列下耦合系统的减振机制，提高减振器的减振效果。以桥梁梁体与减振器的空间耦合振动为研究对象，构建空间耦合振子系统模型；应用稳定性分析方法，确定频率空间重排后该系统达到稳态所需的临界耦合强度，并结合统计理论探索与所有频率空间排列对应的临界耦合强度所服从的分布；进而寻找与频率空间排列相关的参量，揭示该参量与临界耦合强度的分布间的关联，得到该分布的普适规律及其内在机制。最终确定最小成本下，耦合振子系统实现减振的最优频率空间排列。本课题的研究对桥梁、道路和建筑等的减振和控制具有现实的指导意义。

强烈振动严重危害着工农业生产、科学研究和日常生活，并对广泛采用的阻尼减振器的性能提出了很大的挑战。本项目通过探索阻尼减振器的频率空间排列对耦合振子系统减振的影响，确定最优频率空间排列下耦合系统的减振机制，提高减振器的减振效果。以减振器的空间耦合振动为研究对象，构建空间耦合振子系统模型；应用稳定性分析方法，确定频率空间重排后该系统达到稳态所需的临界耦合强度，并结合统计理论探索与所有频率空间排列对应的临界耦合强度所服从的分布；进而寻找与频率空间排列相关的参量，揭示该参量与临界耦合强度的分布间的关联，得到该分布的普适规律及其内在机制。最终确定最小成本下，耦合振子系统实现减振的最优频率空间排列。经过四年努力，在国际和国内主流物理学刊物上已经发表SCI收录论文15篇左右，其中包括Physics Rev. E 1篇，Scientific Reports 1篇，Plos one 1 篇，Chaos 2篇，Europhysics Letters 2篇，Nonlinear Dynamics 2篇,Communications in Nonlinear Science & Numerical Simulation 2 篇， 其它4篇。该项目资助下，项目成员1人获得江西省青年科学培养对象人才项目资助，1 人获得江西省杰出青年人才资助计划项目。