双稳态结构中的1/2次谐波共振及其对隔振特性的影响  

1/2 sub-harmonic resonance in bistable structure and its effect on vibration isolation characteristics

作　　者：刘恩彩 方鑫 温激鸿[1] 郁殿龙[1] Liu En-Cai;Fang Xin;Wen Ji-Hong;Yu Dian-Long(Key Laboratory of Science and Technology on Integrated Logistics Support,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学装备综合保障技术重点实验室

出　　处：《物理学报》2020年第6期124-135,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:51875569,11872371)资助的课题~~

摘　　要：以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.In the extensive modern applications,the low-frequency and heavy-load isolators are needed to reduce the vibration transmissions.The unique properties of nonlinear systems,such as jumping,bifurcation and chaos,provide new ideas for designing the new functional structures.Bistable system is a typical non-linear system,features highly static and low dynamic stiffness,which promises to realize a low-frequency isolator with ensuring heavy load capacity.However,more studies are necessary to clarify the sub-harmonic resonance and its generation process,parameter influences,vibration isolation characteristics of the bistable structure.By adopting the equivalent,analytical,numerical and experimental methods,we study the 1/2 subharmonic resonance,evolution process and its influence on the vibration isolation characteristics of the bistable structure in this paper.When the amplitude or nonlinear stiffness coefficient kn increases to a certain extent,1/2 sub-harmonic resonance appears,where the response contains high-amplitude w/2 component under the excitation frequency w,so the energy is transferred from high frequency to low frequency.We study the bifurcation and varying processes of the fundamental and 1/2 sub-harmonic transmission by increasing the amplitude.At critical bifurcation amplitude,the sub-harmonic transmission rapidly increases from 0 to a large peak value.And then,it decreases gradually when the damping is absent.However,the peak value of 1/2 subharmonic does not cause the fundamental transmission to change suddenly.When considerable damping appears with the increase of the amplitude,1/2 sub-harmonic does not always exist,instead,it follows an interesting“generation-enhancement-degeneration-disappearance”process.This process possesses great significance in applying the 1/2 sub-harmonic to vibration manipulation or avoiding the resonant enhancement induced by it.Moreover,in this process,both the peak frequency and the peak transmission of the bistable isolation system descend first.The optimal combinatio

关 键 词：双稳态结构 次谐波共振 隔振 屈曲梁 

分 类 号：O32[理学—一般力学与力学基础]