Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Nonlinear vibration analysis of a two-degree of freedom system at simultaneous resonance

Authors
Somaye Ahmadsani
Hasan Nahvi
Abstract
To accurately predict vibration behavior of structures, a complete mathematical modeling is necessary. In nonlinear structural vibration analysis, using the linear model may lead to wrong results. In this paper, the nonlinear vibrations of a two-degree-of-freedom system consists of the main system and an absorber is studied at simultaneous secondary and internal resonances. The frequency response equations are obtained by solving the equations of motion using the method of multiple time scales (MTS). The effects of system parameters on the amplitude of the main system is investigated. Stability analysis is performed by the method of Andronov and Vitt and the saddle-node bifurcation points are detected. The results show that in the simultaneous super-harmonic and internal resonance case, system shows an almost linear behavior. Also, the nonlinear parameters of the absorber have insignificant effect on the amplitude of the main system. Unlike the linear case, when the nonlinear stiffness of the main system increases, the system amplitude increases as well. Finally, the domain of detuning parameter with three responses, resulted in the jump phenomenon in the response, is determined.
Keywords
Nonlinear vibration
Absorber
Multiple time scale method
Super-harmonic resonance
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Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 16, Issue 1 - Serial Number 34
System Dyanamics and Solid Mechanics
Spring 2014
Pages 21-42

  • Receive Date 22 May 2014