基于非线性能量吸振器的高耸结构减振分析

摘要

非线性能量阱（NES）类型的振子具有宽频吸振的特性，可利用其对高耸结构进行减振。通过建立相应的偏微分运动方程，并利用伽辽金法及Rauscher方法，获得了非线性模态的解析解，揭示了NES振子的吸振原理。再通过非线性有限元分析，对该系统振动特性随NES振子各参数的变化进行了研究。研究结果表明：NES振子存在最优参数从而明显地抑制结构振动，最大可使结构振动减为原来的20％左右；所提出的经验公式可方便地计算NES振子立方非线性刚度系数的最优值，且与有限元计算结果吻合。%Nonlinear energy sink (NES)absorber has a critical feature of mitigating vibrations in a broad frequency range,it can be utilized in vibration reduction of tall structures.Here,partial differential equations governing a tall structure system motion were built,the analytic solutions of nonlinear normal modes were achieved by applying Galerkin's method and Rauscher's method.The nonlinear normal modal analysis revealed the vibration suppression principle of a NES absorber.The vibration characteristics of a NES-structure system were studied with varying of parameters of a NES absorber suing the nonlinear finite-element-method (FEM). Results indicated that a NES absorber has optimal parameters,with those the structure vibration is greatly suppressed,the structure vibration with a NES absorber is reduced to 20% of the original one without a NES absorber,i.e.,80% of the vibration is suppressed;the empirical formula proposed is capable of predicting the optimal cubic stiffness values of a NES absorber,the value agree well with those obtained via FEM.