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采用连续体系统动力学分析方法对一类平面单塔斜拉桥的固有频率及模态进行了计算与分析。桥面两端简支,并由一个刚性的塔和两根斜拉索支撑。将桥面简化成梁的模型,建立了各斜拉索及各梁段的动力学偏微分方程、斜拉桥的边界条件及子结构间的几何与力学相容条件。推导了斜拉桥线性化、无阻尼系统的频率方程。考虑斜拉桥左右对称及参数(斜拉索长度、初始垂度)微小变动导致对称性破缺的情况,数值求解不同参数下斜拉桥的固有频率及对应的模态。结果表明:斜拉桥第3阶和第4阶固有频率相差不到0.1%,具有密集固有频率的现象;斜拉桥对称性破缺前后第3阶和第4阶固有频率随参数变化的曲线具有频率曲线偏转现象,第3阶和第4阶模态间存在模态跃迁现象。该研究结果可在斜拉桥设计和建造过程中起参考作用。
The natural frequency and modal of a kind of planar single tower cable-stayed bridge are calculated and analyzed by continuum system dynamics analysis method. The ends of the deck are simply supported and supported by a rigid tower and two stay cables. The bridge deck is simplified into a beam model, and the dynamic partial differential equations of each stay cable and each beam section, the boundary conditions of the cable-stayed bridge and the geometry and mechanics compatibility between substructure are established. The frequency equation of linearized and undamped system is deduced. Considering the left and right symmetry of the cable-stayed bridge and the slight variation of the parameters (the length of the stay cables and the initial dip), the natural frequency and the corresponding modes of the cable-stayed bridge are numerically solved. The results show that the difference between the natural frequencies of the third and fourth order of cable-stayed bridges is less than 0.1%, which has the phenomenon of dense natural frequency. The curve of the natural frequencies of the third and fourth order before and after the symmetry breaking of the cable-stayed bridge changes with the parameters With frequency curve deflection phenomenon, there is mode transition phenomenon between the 3rd and 4th modes. The results of this study can be referenced in the design and construction of cable-stayed bridges.