FREQUENCY ANALYSIS OF NONLINEAR FREE VIBRATION OF A CROSS STRING

This work concerns nonlinear free vibration of a cross string with large amplitude. The equations governing the nonlinear vibration of the cross string are derived firstly from Hamilton Principle, which take the form of Duffing equation. Then the perturbation method is used to solve the non-linear coupling natural frequency of the cross string. Our results show that the frequency of the cross string is affected by the vibration amplitude, the cross-section diameter and the ratio of the string length. And the nonlinear coupling natural frequency not only has the characteristic of nonlinearity, but also reflects the coupling property. That is to say, the frequency of the cross string will change when its part changes, however, the changing amplitude is smaller than that of the sub-structures. This indicates that the coupling characteristic can increase the stability of the whole cross string.