Forced Vibration of Air Spring with Asymmetric Nonlinear Restoring Force —System Excited by Motion of Support Point—

In this paper, an experimental and theoretical investigation has been made for the forced vibration of one-degree-of-freedom with asymmetric nonlinear restoring force. Forced vibration of nonlinear air spring excited by motion of support point is taken up, and the characteristics of stationary solution for this system is analyzed by means of catastrophe theory. The validity of theoretical analysis is confirmed by the experiment using a diaphragm air spring. As a result, it is clarified that the characteristics of this system can be described by the cusp catastrophe model. This means that the jump phenomenon of amplitude for the displacement of mass or the relative displacement is controlled by the excitation angular frequency and the amplitude of excitation displacement of support point. In other words, the jump phenomenon (including hysteresis phenomenon) is explained by the bifurcation set, which shows the relationship between the excitation angular frequency and the amplitude of excitation displacement of support point.