中文摘要：

为得到同时考虑弯曲刚度和垂度影响的拉索面内模态的理论公式,首先推导出在整体割线坐标系下考虑弯曲刚度和垂度效应斜索的运动方程式,然后基于扁平索假定和Irvine的拉索初始形状方程推导了扁平斜索的固有频率和振型的理论计算公式。通过与有限差分法得到的精确解的对比表明,考虑弯曲刚度的拉索面内固有振动的理论计算公式能较准确地计算出水平索和斜索的面内固有振动频率和振型。

英文摘要：

In order to obtain the theoretical equations of in-plane modes for cables considering bending stiffness and sag effect, the equations of motion for inclined cable considered bending stiffness is derived in the local coordinate system first. Then, based on the assumption of flat-sag cable and the initial shape function of cable suggested by Irvine, the theoretical calculation equations for in-plane natural frequencies and modal shapes of flat-sag inclined cables are derived. Compared with the exact results obtained by finite difference method, the proposed formulas can be reliably applied to calculate the in-plane frequencies and mode shapes of natural vibration, both for horizontal cable and inclined cable.