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Parametric resonance occurring in many mechanical systems has a special resonance mechanism compared with external resonance, and it is usually produced under the excitation, whose direction is not parallel to the motion direction of the system. In this paper, we clarify that parametric resonance can be induced also under the excitation parallel to the motion direction of the system in the case when the system is subjected to asymmetric restoring force. The dependency of the unstable region of the trivial steady state on the magnitude of the asymmetric component is investigated and the steady state under the parametric excitation is examined by nonlinear analysis. Furthermore, we use a simple experimental apparatus of a system subjected to magnetic asymmetric nonlinear restoring force and discuss the validity of the theoretical results.

Parametric Resonance Due to Asymmetric Nonlinearity of Restoring Force