拉索平面内自由振动影响因素分析

考虑抗弯刚度、垂度和几何非线性的影响，建立了拉索非线性自由振动方程，针对考虑与否垂度和几何非线性，分别建立了线性无垂度和有垂度理论、非线性无垂度和有垂度理论，用谐波平衡法求得拉索振动固有频率的近似解析解。其结果与龙格-库塔积分法得到的结果较为一致。此外，还给出了抗弯刚度、垂度和几何非线性对拉索振动固有频率影响的定量判定。

Analysis of Influencing Factors on Free In-Plane Vibration of Tensile Cable

The governing equations of non linear free vibration of a horizontal c able were presented considering the effects of the bending stiffness, sag and th e geometric nonlinearity. Those partial differential equations were then transfo rmed into a set of ordinary differential equations through the Garlerkin method. Aimed at whether to consider the sag and geometric nonlinearity, four kinds of theories were put forward such as linear theory without sag, linear theory with sag, non linear theory without sag and non linear theory with sag. The harmoni c balance method was used to study the approximate analytic solution of the natura l frequency of cable vibration. The results agree well with those derived from t he method of the Runge Kutta integration. Based on the comparative study on the four present theories, the quantitative decision was proposed to evaluate the in fluence of the bending stiffness, sag and nonlinearity on the natural frequency.