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Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

  • Jiren Xue
  • Yewei ZhangEmail author
  • Hu Ding
  • Liqun Chen
Article
  • 13 Downloads

Abstract

The nonlinear behaviors and vibration reduction of a linear system with nonlinear energy sink (NES) are investigated. The linear system is excited by a harmonic and random base excitation, consisting of a mass block, a linear spring, and a linear viscous damper. The NES is composed of a mass block, a linear viscous damper, and a spring with ideal cubic nonlinear stiffness. Based on the generalized harmonic function method, the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system. The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions. The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities, the transmissibility transition probability density, and the percentage of the energy absorption transition probability density of the linear oscillator. The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio. The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters, which will affect the stability of the system.

Key words

nonlinear energy sink (NES) Gauss-Legendre polynomial transmissibility percentage of energy absorption 

Chinese Library Classification

O322 

2010 Mathematics Subject Classification

34A34 74K30 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai University, School of Mechanics and Engineering ScienceShanghaiChina
  2. 2.Faculty of Aerospace EngineeringShenyang Aerospace UniversityShenyangChina

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