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

• Published in: Applied mathematics and mechanics Vol. 45; no. 8; pp. 1335 - 1352
• Main Authors: Wan, Honglin, Li, Xianghong, Shen, Yongjun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024; Springer Nature B.V; School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China; Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China%Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China; State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China%State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
• Edition: English ed.
• Subjects: Absorbers; Amplitudes; Applications of Mathematics; Classical Mechanics; Eigenvalues; Exact solutions; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Periodic variations; Qualitative analysis; Stability; Stiffness; Trajectory analysis; Vibration analysis; Vibration control; Vibration response; O323; 34E13; two-scale system; inerter; dynamic vibration absorber; vibration control; O328
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-024-3138-9

The dynamic vibration absorber with inerter and grounded stiffness (IG-DVA) 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.