Application of catastrophe theory to forced vibration of a diaphragm air spring

An experimental and theoretical investigation is presented for the forced vibration of a one-degree-of-freedom system with a non-linear restoring force. Catastrophe theory is applied to the analysis of Duffing's equation. As an example of a case of an asymmetric non-linear restoring force, the forced vibration of a non-linear air spring excited by the motion of the support point is considered, and the characteristic of the stationary solution for this system is analyzed similarly. The validity of these theoretical analyses has been confirmed by a diaphragm air spring experiment, which has shown that the characteristics of these systems can be described by the cusp catastrophe model. The jump phenomenon (including the hysteresis) of the displacement amplitude of the mass is explained by the bifurcation set, which shows the relationship between the excitation radian frequency and the excitation displacement amplitude of the support point (or the amplitude of the excitation force).