Vibration and Bifurcation Analysis of a Nonlinear Damped Mass Grounded System

Subject Areas : Engineering

M Mostoufi ¹ , H Nahvi ² , B Mirshafiee ³

1 - Department of Mechanical Engineering, Isfahan University of Technology
2 - Department of Mechanical Engineering, Isfahan University of Technology
3 - Department of Mechanical Engineering, Isfahan University of Technology

Received: 2013-09-01 Accepted : 2013-11-17 Published : 2014-03-30

Keywords: Nonlinear vibration, Bifurcation, Mass grounded system, Multiple time scale,

Abstract :

In this paper, vibrations and bifurcation of a damped system consists of a mass grounded by linear and nonlinear springs and a nonlinear damper is studied. Nonlinear equation of motion is derived using Newton’s equations. Approximate analytical solutions are obtained using multiple time scales (MTS) method. For free vibration, the approximate analytical results are compared with the numerical integration results. Forced vibrations of the system in primary and secondary resonant cases are studied and the effects of different parameters on the frequency-responses are investigated. Moreover, bifurcation of the system is studied considering different control parameters.

References:

[1] Meirovitch L., 1975, Elements of Vibration Analysis, McGraw-Hill, New York.
[2] Dimarogonas A., 1996, Vibration for Engineers, Prentice-Hall, Englewood Cliffs, NJ.
[3] Telli S., Kopmaz O., 2006, Free vibrations of a mass grounded by linear and nonlinear springs in series, Journal of Sound and Vibration 289:689-710.
[4] Sun W.P., Wu B.S., 2008, Large amplitude free vibrations of a mass grounded by linear and nonlinear springs in series, Journal of Sound and Vibration 314:474-480.
[5] Wu B.S., Li P.S., 2001, A method for obtaining approximate analytic periods for a class of nonlinear oscillators, Meccanica 36:167-176.
[6] Lai S.K., Lim C.W., 2007, Accurate approximate analytical solutions for nonlinear free vibration of systems with serial linear and nonlinear stiffness, Journal of Sound and Vibration 307:720-736.
[7] Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, John Wiley & Sons Inc., New York.