Acta Mechanica

, Volume 230, Issue 7, pp 2563–2579 | Cite as

On the analysis of nonlinear dynamic behavior of an isolation system with irrational restoring force and fractional damping

  • Y. Y. DongEmail author
  • Y. W. Han
  • Z. J. ZhangEmail author
Original Paper


An archetypal isolation system with rational restoring force and fractional damping is proposed and investigated based on the nonlinear mechanism of geometric kinematics. The equations of motion of this nonlinear isolator subject to nonlinear damping and external excitation are derived based on the Lagrange equation. For the free vibration system, the nonlinear irrational restoring force, nonlinear stiffness behaviors, and fractional damping are investigated to show the complex transitions of multi-stability. For the forced vibration system, the analytical expressions of force transmissibility of the nonlinear isolator with single-well potential under the perturbation of viscous damping and harmonic forcing are formulated by applying the harmonic balance method. The shock response spectra of the perturbed system subject to half-sine input are evaluated by the maximum responses. The Melnikov analysis and empirical method are employed to determine the analytical criteria of chaotic thresholds for the homoclinic orbit of the perturbed system with symmetric double-well characteristics. The numerical simulations are carried out to demonstrate periodic solutions, periodic doubling bifurcation, and chaotic solutions. The maximum displacements have been obtained to show the isolation characteristics in the case of chaotic vibration.



The authors would like to acknowledge the Fundamental Research Funds for the Central Universities, No. NS2018055.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AstronauticsNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Civil EngineeringHenan University of Science and TechnologyLuoyangChina

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