OICC Press Journal of Solid Mechanics 2008-7683 6 1 2014 03 30 Vibration and Bifurcation Analysis of a Nonlinear Damped Mass Grounded System 1 18 EN M Mostoufi Department of Mechanical Engineering, Isfahan University of Technology H Nahvi Department of Mechanical Engineering, Isfahan University of Technology B Mirshafiee Department of Mechanical Engineering, Isfahan University of Technology Journal Article 2014 03 30 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.