双稳态余弦梁非线性隔振器的动力学与隔振特性研究  

Dynamics and isolation performance of a nonlinear vibration isolator with a bistable cosine-shaped beam

作　　者：张威[1,2] 王文波 李双宝 ZHANG Wei;WANG Wenbo;LI Shuangbao(College of Aeronautical Engineering,Civil Aviation University of China,Tianjin 300300,China;CAAC Aviational Ground Special Equipment Research Base,Tianjin 300300,China;College of Science,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学航空工程学院,天津300300 [2]中国民航航空地面特种设备研究基地,天津300300 [3]中国民航大学理学院,天津300300

出　　处：《振动与冲击》2022年第2期113-122,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金委员会与中国民航局联合资助项目(U2033208,U1533103);国家自然科学基金面上项目(12172376,11672326);天津市研究生科研创新项目(2019YJSS081)。

摘　　要：为了隔离航空器上的低频振动,提出一种具有准零刚度特性的非线性隔振器,由线性正刚度弹簧并联双稳态余弦梁负刚度元件而成。首先,通过对余弦梁非线性隔振器的静力学分析,给出了隔振器在准零刚度平衡点时的结构参数需要满足的条件。其次,建立谐波力作用下的系统动力学模型,通过未扰系统的分析,得到其存在平衡点分岔行为和满足稳定准零刚度的条件。最后,通过数值方法和有限元软件动力学仿真分析扰动系统的隔振性能,得到余弦梁非线性隔振器的起始隔振频率。进一步与线性隔振系统相比可知,引入余弦梁的非线性隔振系统有效降低了起始隔振频率。因此,余弦梁非线性隔振器具有优异的低频隔振性能,这为低频非线性隔振器设计提供了理论基础。In order to isolate the low frequency vibrations in aircraft,a quasi-zero stiffness nonlinear vibration isolator was proposed,which is composed of a linear positive stiffness spring and a parallel connected bistable cosine-shaped beam with negative stiffness.Firstly,through the static analysis of the cosine-shaped beam nonlinear vibration isolator,the conditions that the structural parameters of the isolator should be satisfied at the quasi-zero-stiffness equilibrium point were given.Then,the dynamical model of a harmonically excited nonlinear vibration isolator with a bistable cosine-shaped beam was established.Through the analysis of the unperturbed system,the existence of bifurcation behavior of the equilibrium point was proved and the condition of stable quasi-zero-stiffness was obtained.Finally,the isolation performance of the cosine-shaped beam nonlinear isolator under the excitation force was analyzed to obtain the initial vibration isolation frequency by using numerical analysis method and finite element analysis.Comparing with the linear vibration isolation system,it is shown that the initial vibration isolation frequency can be effectively reduced by the proposed quasi-zero stiffness nonlinear vibration isolator with cosine-shaped beam.Therefore,the proposed hybrid vibration isolator has excellent low frequency vibration isolation performance,which provides a theoretical basis for the optimal design of the low frequency nonlinear vibration isolator.

关 键 词：双稳态余弦梁 平衡点分岔 起始隔振频率 准零刚度 

分 类 号：TH212[机械工程—机械制造及自动化]