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斜拉桥面内竖向固有振动模型及特性影响的有限差分分析
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Influence Analysis on In-plane Vertical Natural Vibration Model of Cable-stayed Bridges Based on Finite Difference Method
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    摘要:

    为研究精确且方便的斜拉桥面内竖向模态频率及振型计算方法,建立了用于模拟斜拉桥面内竖向固有振动行为的主梁集中质量参数体系动力学模型. 该模型考虑了拉索对主梁的竖向弹性支承作用及对主梁不同截面的水平索力投影,通过引入微梁段两侧剪力以模拟主梁弯曲刚度、拉索间运动耦合作用. 基于微梁段间的弯矩平衡和有限差分法,得到了不同体系斜拉桥面内竖向固有振动的频率方程和振型函数,编制了求解程序. 通过分别代入相关研究中算例参数、某斜拉桥参数并对比模态参数理论计算结果、实测频率值,验证了本文建模方法及公式的精确度、适用性. 参数分析结果表明:斜拉桥低阶面内竖向频率受主梁轴力影响较大,轴力增大后会发生低阶频率的跃迁现象;发生断索对各阶频率值的影响效应与拉索锚固处主梁质点的对应阶次振型参与系数相关.

    Abstract:

    To propose a precise and convenient solution method for in-plane vertical modes of cable-stayed bridges, a new dynamic model comprised of lumped mass beam segments was established in this paper, which was used to simulate the in-plane vertical natural vibration behavior of cable-stayed bridges. In the model, the cables were reduced to vertical elastic supports and external forces on the girder in the horizontal direction. Additionally, the shear forces on both sides of the micro beam-segment were introduced to simulate the actions of the beam’s bending stiffness and the coupled interaction between the cables. Based on the moment equilibrium between the beam segments and the finite difference method, the solutions of the in-plane vertical modal frequencies and shapes of cable-stayed bridges of different systems can be obtained. A computational solution program was also developed. The theoretical solutions were compared to field-test results from an actual bridge, confirming that the model and method proposed in this paper can accurately calculate the modal properties of in-plane vertical modes of cable-stayed bridges. The results through parametric analysis showed that the effect of the beam’s axial force was more significant on the low-order modal. The phenomenon of a transition on the low-order mode was observed when the axial force was increased to a high value. Moreover, when the cable is broken, the influence on each mode is related to the corresponding mode participation coefficient of the beam segment anchored with the cable.

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陈柯帆 ,李源 ?,贺拴海 ,王康 ,殷怡萍 ,宋一凡 .斜拉桥面内竖向固有振动模型及特性影响的有限差分分析[J].湖南大学学报:自然科学版,2023,(7):33~43

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  • 在线发布日期: 2023-07-31
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