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在Rayleigh能量法和Southwell’s频率合成法的基础上,将悬索桥裸塔的振动基频表示成由各变形元和惯性元组成的子系统频率的合成,通过挠度函数的合理选取,导出了悬索桥裸塔振动基频的近似算法。以泰州大桥钢中塔为计算实例,分析了顶部附加质量比、结构自身剪切变形、承台振动对基频的影响。数值计算与实桥现场环境振动试验表明,桥塔振动基频会随顶部附加质量比增大而减小,忽略剪切变形对计算结果影响甚微,但承台的振动不可忽略。该方法不仅适用于底部固定以及顶端带有附加质量的塔式结构,也适用于其他截面复杂的高层建筑、烟囱等高耸工程结构。
Based on the Rayleigh energy method and the Southwell’s frequency synthesis method, the fundamental vibration frequency of the bare tower of the suspension bridge is expressed as the synthesis of the subsystem frequencies composed of the deformable elements and the inertial elements. The reasonable selection of the deflection function leads to the suspension tower Approximate Algorithm of Vibration Fundamental Frequency. Based on the calculation of Taichung Steel Tower in Taizhou Bridge, the influence of the additional mass ratio at the top, the shear deformation of the structure itself and the vibration of the bearing platform on the fundamental frequency is analyzed. The numerical calculation and the vibration test of the actual bridge site environment show that the fundamental frequency of the bridge tower decreases with the increase of the top additional mass ratio. Ignoring the shear deformation has little effect on the calculation results, but the vibration of the platform should not be neglected. This method is not only suitable for fixed bottom structure and tower structure with additional mass at the top, but also for other high-rise structures such as high-rise buildings and chimneys with complicated sections.