On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator

There are many systems which consist of a nonlinear oscillator attached to a linear system, examples of which are nonlinear vibration absorbers, or nonlinear systems under test using shakers excited harmonically with a constant force. This paper presents a study of the dynamic behaviour of a specific two degree-of-freedom system representing such a system, in which the nonlinear system does not affect the vibration of the forced linear system. The nonlinearity of the attachment is derived from a geometric configuration consisting of a mass suspended on two springs which are adjusted to achieve a quasi-zero stiffness characteristic with pure cubic nonlinearity. The response of the system at the frequency of excitation is found analytically by applying the method of averaging. The effects of the system parameters on the frequency-amplitude response of the relative motion are examined. It is found that closed detached resonance curves lying outside or inside the continuous path of the main resonance curve can appear as a part of the overall amplitude-frequency response. Two typical situations for the creation of the detached resonance curve inside the main resonance curve, which are dependent on the damping in the nonlinear oscillator, are discussed.