复合干摩擦的准零刚度隔振系统的亚谐共振  

SUBHARMONIC RESONANCE OF QUASI-ZERO-STIFFNESS VIBRATION ISOLATION SYSTEM WITH DRY FRICTION DAMPER

作　　者：牛江川[1,2] 张婉洁 申永军 王军[1,2] Niu Jiangchuan;Zhang Wanjie;Shen Yongjun;Wang Jun(State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学交通工程结构力学行为与系统安全国家重点实验室,石家庄050043 [2]石家庄铁道大学机械工程学院,石家庄050043

出　　处：《力学学报》2022年第4期1092-1101,I0005,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11872254,U1934201,11802183);河北省自然科学基金(A2021210012)资助项目。

摘　　要：利用增量平均法研究了复合干摩擦阻尼器的准零刚度非线性隔振系统在外部简谐激励作用下的1/3次亚谐共振.首先利用平均法得到了复合干摩擦的准零刚度隔振系统的主共振近似解析解,然后在系统主共振近似解析解的基础上将系统的亚谐共振响应看作增量,并利用平均法得到了准零刚度隔振系统的亚谐共振近似解析解.利用李雅普诺夫方法得到了准零刚度隔振系统主共振和亚谐共振稳态解的稳定性条件,并推导了系统1/3次亚谐共振的存在条件.根据近似解析解分别得到了复合干摩擦的准零刚度隔振系统的主共振和亚谐共振力传递率.利用数值解验证了准零刚度隔振系统主共振和亚谐共振近似解析解的准确性.利用系统的近似解析解详细分析了准零刚度参数和干摩擦力对系统主共振和亚谐共振的幅频响应以及力传递特性的影响.分析结果表明,通过选取合适的干摩擦力参数,可以消除准零刚度隔振系统在主共振区域的亚谐共振.通过复合干摩擦阻尼器不但可以提高准零刚度隔振系统在低频区域的振幅抑制效果,而且可以降低准零刚度隔振系统的起始隔振频率,但是会增大系统在有效隔振频带内的力传递率.The 1/3 subharmonic resonance of the quasi-zero-stiffness nonlinear vibration isolation system with dry friction damper is studied by using the incremental averaging method,which is subjected to external simple harmonic excitation.Firstly,the approximate analytical solution of the primary resonance of the quasi-zero-stiffness vibration isolation system with dry friction damper is obtained by using the averaging method.Then,based on the approximate analytical solution of the primary resonance of the system,the subharmonic resonance response of the system is regarded as an increment,and the approximate analytical solution of the subharmonic resonance of the quasi-zero-stiffness vibration isolation system is obtained by using the averaging method.The stability conditions of the steady-state solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system are obtained by using the Lyapunov method,and the existence condition of the 1/3 subharmonic resonance of the quasi-zero-stiffness vibration isolation system is deduced.According to the approximate analytical solution,the primary resonance and subharmonic resonance force transmissibility of the quasi-zero-stiffness vibration isolation system with dry friction damper are obtained respectively.Compared with the numerical solution,the accuracy of the approximate analytical solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system is verified.By using the approximate analytical solution of the system,the effects of quasi-zero stiffness parameters and dry friction force on the amplitude-frequency response and force transfer characteristics for the primary resonance and subharmonic resonance of the system are analyzed in detail.The results show that the subharmonic resonance of the quasi-zero-stiffness vibration isolation system in the primary resonance region can be eliminated by selecting appropriate dry friction force parameter.The addition of dry friction dampe

关 键 词：亚谐共振 准零刚度 隔振 干摩擦 

分 类 号：O322[理学—一般力学与力学基础]