自锚式斜拉-悬索协作体系竖向弯曲振动计算公式

Estimation Frequency Formulas of Vertical Vibration for Self-anchored Cable-suspension Bridge

为方便计算自锚式斜拉-悬索协作体系的竖向自振频率,以三跨连续协作体系为研究对象,在计入主塔刚度的影响下,应用Rayleigh法,推导了该体系的竖向弯曲振动频率公式,提出了主塔刚度影响系数的表达式,最后对此公式的可行性进行了算例验证.研究结果表明:该体系的竖向弯曲振动频率比同等结构布置的自锚式悬索桥的竖向弯曲频率略有增大;主塔刚度对该体系的一阶对称竖弯频率影响较大,进行此频率计算时应计入主塔刚度的影响,而对一阶反对称竖弯无影响;给出的能量法得到的竖弯基频计算值与有限元值误差能满足概念设计阶段的要求;该公式可用于自锚式斜拉-悬索协作体系在初步概念设计中选择合理的结构计算参数.

To calculate vertical frequency of the self-anchored hybrid cable-suspension bridge conveniently,the self-anchored hybrid cable-suspension bridge with double-tower was taken as research object. Frequency formulas for the first symmetric and asymmetric vertical vibration modes were induced by the Rayleigh method and the influence of coefficient for tower stiffness was proposed. Finally,the presented analytic formulas were validated by the engineering project. The results indicate that the vertical vibration frequency of self-anchored hybrid cable-suspension bridge is slightly higher than that of the self-anchored suspension bridge. Tower stiffness which should be correctly considered in frequency calculation has a great influence on the first symmetric vertical frequency,while it has no effect on the first asymmetric vertical frequency. The error between values calculated by the proposed formulas and the finite element method（ FEM） meets with the requirement of conceptual design. The proposed formulas can be applied to select reasonable parameters for the self-anchored cable-suspension bridge in conceptual design stage.