中文摘要：

为方便计算多塔斜拉桥的竖向自振频率，基于最简单的多塔斜拉桥形式———三塔斜拉桥，考虑主塔刚度对振动频率的影响，应用Rayleigh法，给出主梁竖向自由振动的振型函数和主塔纵向自由振动的振型函数，并推导出考虑主塔刚度影响的三塔斜拉桥竖弯振动频率公式，且对其精确性进行多个算例验证。研究结果表明：主塔刚度对于三塔斜拉桥竖弯刚度影响较大，频率计算时应予以考虑，给出的能量法得到的纵飘基频计算值与有限元值误差比规范解与有限元值误差小，该公式能满足概念设计阶段的要求，适用于三塔斜拉桥的振动基频估算。

英文摘要：

In order to calculate fundamental frequency of the cable -stayed bridges with multi -tower conveniently, the cable-stayed bridges with three tower was taken as research object. Frequency formula for vi-bration mode of cable-stayed bridges was induced by the Rayleigh method and vibration mode function of vertical free vibration of main beam and vibration type function of longitudinal free vibration of main tower were intro-duced. The practical vertical frequency formula for vibration of cable-stayed bridges with three tower considering tower stiffness influence was then derived. Finally, the presented theoretical formula of fundamental frequency was found to be valid in engineering and the frequency formula for vibration was discussed therein. The results in-dicate that section types of the girder, tower and cable has no influence on the vertical frequency formula for vi-bration of cable-stayed bridges, but the tower stiffness has a great influence on vertical frequency of cable-stayed bridges. The constrain condition and tower stiffness should be carefully considered in the calculation of fre-quency. The fundamental frequency calculated by the recommended method has a smaller error compared with the finite element method （ FEM） result, which satisfies the requirement of conceptive design. The presented theoret-ical formula can be applied to the estimation of frequency for vibration of cable-stayed bridges with three tower.