Theoretical Analysis for Force Transmissibility and Jump Phenomena of Duffing Spring Type Vibration Isolator


Article Preview

In order to study the common nonlinear characteristics of the vibration isolator, a single degree of freedom system with cubic restoring force is introduced to describe the nonlinear vibration isolation system in the paper and the harmonic balance method was applied to investigate the primary resonance near the natural frequency of the system. Based on Routh–Hurwitz stability criterion, it was clarified theoretically that the region surrounded by the curve of the vertical tangential points in the curve cluster of the primary resonance amplitude frequency characteristics was instable. In addition, the equations of the jump frequency and force transmissibility were derived. The calculated results showed that the jump, hysteresis, stable and instable phenomena would take place for the force transmissibility of the isolator system and the effect of high frequency components of the transmitting force was limited; the damping, coefficient of nonlinear restoring force and the excitation amplitude had an influence on the force transmissibility whose frequencies were in the region of the resonance frequencies but not on those whose frequencies were lower than the resonance frequencies, and only the damping would affect the force transmissibility whose frequencies were higher than the resonance frequencies. Finally, the equation of the start frequency, on the condition that the force transmissibility was less than 1, was presented.



Edited by:

Jing Guo




X. L. Zhang et al., "Theoretical Analysis for Force Transmissibility and Jump Phenomena of Duffing Spring Type Vibration Isolator", Applied Mechanics and Materials, Vol. 224, pp. 11-17, 2012

Online since:

November 2012




[1] Yoshikazu Araki, Takehiko Asai and Takeshi Masui: Vertical vibration isolator having piecewise-constant restoring force. Earthquake Engineering & Structural Dynamics Vol. 38(2009), pp.1505-1523.


[2] R.A. Ibrahim: Recent advances in nonlinear passive vibration isolators. Journal of Sound and Vibration Vol. 314 (2008) pp.371-452.


[3] Ivana Kovacic, Michael J. Brennan and Timothy Waters: A study of a nonlinear vibration isolator with a quasi-zero stiffness characteristic. Journal of Sound and Vibration Vol. 315 (2008) pp.700-711.


[4] Chen Yongbin and Chen Shuhui: The Response and Transmissibility of Nonlinear Isolating Systems. Journal of Vibration and Shock Vol. 17(1998) pp.18-22.

[5] Chen Anhua, Liu Deshun and Zhu Pingyu: Nonlinear Response Analysis of a Passively Vibration- Isolated Body. Chinese Journal of Mechanical Engineering Vol. 37(2001) pp.99-101.


[6] Zhou Yifeng, Tang Jinyuan and He Xuhui: Response and Transmissibility of Strong Nonlinear Active Isolation System. Journal of Central South University (Science and Technology) Vol. 36(2005) pp.496-500.

[7] A. Carrella, M.J. Brennan and T.P. Waters. Force transmissibility of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. Sixth EUROMECH Nonlinear Dynamics Conference, June 30 — July 4, 2008, Saint Petersburg, RUSSIA.