Study on vibration reduction of two-scale system coupled with dynamic vibration absorber  

作　　者：Honglin WAN Xianghong LI Yongjun SHEN 

机构地区：[1]Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China [2]State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China [3]School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第8期1335-1352,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12172233 and U1934201)。

摘　　要：The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of the main system coupled with absorber is significantly reduced,and the high frequency vibration completely disappears.First,through the slow-fast analysis and stability theory,it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system.After adding the dynamic vibrator absorber,the center in the autonomous system changes to an asymptotically stable focus,consequently suppressing the vibration in the non-autonomous system.Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system,thereby regulating the stability of the system.Transitioning from a qualitative standpoint to a quantitative approach,a comparison of the solutions before and after the introduction of the dynamic absorber reveals that,when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal,the high-frequency part in the analytical solution disappears.As a result,this leads to a reduction in the amplitude of the trajectory,achieving a vibration reduction effect.

关 键 词：two-scale system dynamic vibration absorber vibration control inerter 

分 类 号：O323[理学—一般力学与力学基础] O328[理学—力学]