非线性能量阱系统的强调制响应研究
Investigation on strongly modulated response of nonlinear energy sink system
投稿时间:2021-06-10  修订日期:2021-09-19
DOI:
中文关键词:  非线性能量阱  强调制响应  慢不变流形  复变量平均法  振动抑制
英文关键词:nonlinear energy sink (NES)  strongly modulated response (SMR)  slow invariant manifold (SIM)  complex-averaging method  vibration suppression
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位邮编
柴凯 海军工程大学 430033
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中文摘要:
      针对强调制响应时非线性能量阱的振动抑制效果要比稳态周期响应时更好,开展非线性能量阱系统的强调制响应研究。首先,利用复变量平均法推导主共振下系统的慢变动力流方程;其次,结合多尺度法实现系统的快变流形与慢变流形的分离,得到不同参数下系统的慢不变流形以及全局分岔特性;然后,通过构建快变流形的一维映射函数,揭示非线性能量阱系统呈现强调制响应状态的充分条件和必要条件;最后,搭建非线性能量阱系统的模拟电路,开展强调制响应检测电路试验。仿真和试验结果表明,非线性能量阱系统响应超越慢不变流形上的极值点幅值,又不吸引至慢不变流形某一分支,且形成连续跳跃环路而不陷入局部循环时,强调制响应才出现,为深入理解非线性能量阱系统的强调制响应产生机制及其参数优化提供了理论基础和技术支撑。
英文摘要:
      In view of the vibration suppression effect of the nonlinear energy sink (NES) in the strongly modulated response (SMR) is better than in the steady-state periodic response, the SMR study of the NES system is carried out. Firstly, the equation of systematic slow variation flow equation is derived by using the complex-averaging method. Secondly, the multi-scale method is used to realize the separation of the rapid variable manifold and the slow variable manifold, and the systematic slow invariant manifold under different parameters and the global bifurcation property are obtained. Then, by building the one-dimensional mapping function of the rapid variable manifold, the sufficient and necessary conditions for the NES system in the SMR state are revealed. Finally, the simulation circuit of the NES system is constructed and the response detection circuit test is carried out. The simulation and experimental results show that the response of the NES system exceeds the amplitude of the extremum point on the slow invariant manifold, does not attract to a branch of the slow invariant manifold, and forms a continuous jump loop without falling into a local cycle, only in this way can the SMR state appear. The SMR study of the NES system is provided by the theoretical foundation and technical support for the emphasis on the mechanism and its parameters optimization.
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