Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation
- 13 Downloads
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 wordsnonlinear energy sink (NES) Gauss-Legendre polynomial transmissibility percentage of energy absorption
Chinese Library ClassificationO322
2010 Mathematics Subject Classification34A34 74K30
Unable to display preview. Download preview PDF.
- SU, C., ZHONG, C. Y., and ZHOU, L. C. Random vibration analysis of coupled vehicle-bridge systems with the explicit time-domain method (in Chinese). Applied Mathematics and Mechanics, 38, 107–158 (2017)Google Scholar
- WOJTKIEWICZ, S. F., BERGMAN, L. A., and SPENCER JR, B. F. Robust Numerical Solution of the Fokker-Planck-Kolmogorov Equation for Two Dimensional Stochastic Dynamical Systems, Technical Report AAE 94-08, Department of Aeronautical and Astronautica Engineering, University of Illinois at Urbana-Champaign, Urbana-Champaign (1994)Google Scholar
- KUMAR, M., CHAKRAVORTY, S., and JOHN, J. L. Computational nonlinear stochastic control based on the Fokker-Planck-Kolmogorov equation. American Institute of Aeronautics and Astronautics, 25, 1–15 (2008)Google Scholar