Frequency analysis of nonlinear free vibration of a cross string

Abstract

This work concerns nonlinear free vibration of a cross string under large amplitude. The equations governing the nonlinear vibration of the cross string are derived at first from the Hamilton principle, and they take the form of Duffing equation. Then the perturbation method is used to solve the nonlinear coupled natural frequency of the cross string. The nonlinear natural frequency not only has the characteristic of nonlinearity, but also reflects the coupled characteristic, i.e., the natural frequency of the cross string varying with that of its constituent strings. The results show that the overall effect on the cross string is somehow averaged due to the nonlinearity of each constituent string, i.e., the natural frequencies of the cross string contain both the linear natural frequencies of the constituent strings and the nonlinear parts that depend upon the vibration amplitude, the diameter of one constituent string, the length ratio of the two strings, etc., but the contribution of each constituent string to the natural frequency is in different proportions.