On the analysis of nonlinear dynamic behavior of an isolation system with irrational restoring force and fractional damping
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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.
- 2.Harris, C.M., Paez, T.L.: Shock and Vibration Handbook, 6th edn. McGraw-Hill, New York (2009)Google Scholar
- 13.Ruzicka, J.E., Derby, T.F.: Influence of Damping in Vibration Isolation. The Shock Vib. Inf. Center, Washington (1971)Google Scholar
- 15.Paola, M.D., Mendola, L.L., Navarra, G.: Stochastic seismic analysis of structures with nonlinear viscous dampers. Tsinghua Sci. Technol. 133, 1475–1478 (2007)Google Scholar
- 18.Yan, S., Lin, B., Fei, J., Liu, P.: Nonlinear dynamic behavior of a rotor bearing system with non-linear viscous damping suspension. In: ASME International Mechanical Engineering Congress Exposition, Tampa, USA (2017)Google Scholar
- 23.Li, J., Li, S.: Generating ultra wide low-frequency gap for transverse wave isolation via inertial amplification effects. Phys. Lett. A 383, S0375960117311507 (2017)Google Scholar