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斜梁桥振动频率没有显式解,给使用《公路桥涵设计通用规范》方法计算冲击系数带来不便。考虑斜梁桥振动时的弯扭耦合效应,分别采用修正的Timoshenko梁理论建立其弯曲振动的动态刚度矩阵,采用Saint-Venant扭转理论建立其自由扭转振动的动态刚度矩阵,结合斜支承边界条件,导出斜支承坐标系下的动态刚度矩阵,提取弯矩-转角的刚度方程,根据其奇异条件建立关于斜梁桥自振频率的超越方程,采用二分法对超越方程进行求解以得到自振频率。该文分析了一座标准A型单跨斜箱梁桥考虑与不考虑剪切变形影响时的前5阶振动频率随斜交角的变化,比较了正交简支初等梁和正交简支深梁、斜支初等梁和斜支深梁的前5阶频率。结果显示:斜梁桥基频随斜交角的增大而增大、第2阶频率随斜交角的增大而减小;斜梁桥振动频率的计算应采用考虑剪切变形影响的深梁理论。
The vibration frequency of the inclined beam bridge is not explicitly solved, which brings inconvenience to the calculation of the impact coefficient by the method of “General Specification for Design of Highway Bridges and Culverts”. Considering the flexural and torsional coupling effect of the inclined beam bridge, the dynamic stiffness matrix of bending vibration is established by the modified Timoshenko beam theory and the dynamic stiffness matrix of torsional vibration is established by using the Saint-Venant torsion theory. Combined with the boundary conditions of inclined support, The dynamic stiffness matrix in the inclined support coordinate system is deduced, and the stiffness equation of moment - rotation angle is extracted. Based on the singular conditions, the transcendental equation of the natural frequency of the slant beam bridge is established. The transcendental equation is solved by dichotomy to get the natural frequency. This paper analyzes the variation of the first 5 stages of vibration frequency with the skew angle of a standard single-span inclined box girder bridge with and without considering the effect of shear deformation. By comparing the orthoganal simple beam and the simply supported deep beam, The first 5 orders of primary beam and oblique beam deep beam. The results show that the basic frequency of skew girder bridge increases with the increase of skew angle, and the frequency of the second order decreases with the increase of skew angle. The calculation of vibration frequency of skew girder bridge should adopt the deep beam theory which considers the effect of shear deformation .