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Shock and Vibration
Volume 2014 (2014), Article ID 803275, 12 pages
Research Article

Theoretical Analysis and Numerical Simulation of Resonances and Stability of a Piecewise Linear-Nonlinear Vibration Isolation System

State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 23 February 2013; Accepted 7 August 2013; Published 2 March 2014

Academic Editor: Reza Jazar

Copyright © 2014 X. Gao and Q. Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A methodology is presented to study the resonance and stability for a single-degree-of-freedom (SDOF) system with a piecewise linear-nonlinear stiffness term (i.e., one piece is linear and the other is weakly nonlinear). Firstly, the exact response of the linear governing equation is obtained, and a modified perturbation method is applied to finding the approximate solution of the weakly nonlinear equation. Then, the primary and 1/2 subharmonic resonances are obtained by imposing continuity conditions and periodicity conditions. Furthermore, Jacobian matrix is derived to investigate the stability of resonance responses. Finally, the results of theoretical study are compared with numerical results, and a good agreement is observed.