地震作用下悬浮隧道锚索-管体耦合振动的模型优化与动力分析

MODEL OPTIMIZATION AND DYNAMIC ANALYSIS OF CABLE-TUNNEL COUPLED VIBRATION OF SUBMERGED FLOATING TUNNEL UNDER EARTHQUAKE

  • 摘要: 该文基于Hamilton原理建立了考虑管体转角位移和两侧锚索动张力之差的悬浮隧道锚索-管体耦合振动模型,并通过有限元软件对模型和编写的MATLAB求解程序进行验证。结合已有的悬浮隧道算例对管体和锚索的振动响应进行分析,结果表明:该文所建立的理论计算模型和有限元模型的计算结果具有较好的一致性,可为管体转角位移和扭矩计算提供理论解,并使锚索动张力计算结果更具安全性;管体的转角位移由两侧向中间逐渐增加,但管体在锚索锚固点处的扭矩明显大于其它部位;当锚索受到不对称荷载时,忽略两侧锚索动张力之差会使锚索的振动响应计算结果偏小;在地震荷载下,管体仅奇数阶振型参与振动,偶数阶振型未被激发;利用振型叠加法求解时,为保证计算效率和计算精度,建议跨度500 m及以上的悬浮隧道取7阶以上的模态阶数进行计算,500 m以下的悬浮隧道可取前7阶模态计算。

     

    Abstract: Based on Hamilton principle, a cable-tunnel coupling vibration model of submerged floating tunnel (SFT) is established considering the angular displacement of the tunnel and the difference between the dynamic tensions of cables on both sides. The model and the MATLAB solution program are verified by finite element software. The vibration responses of the tunnel and the cable are analyzed combined with the existing SFT cases. The results show that the theoretical calculation model established in this paper is in good agreement with the finite element model, which can provide theoretical solutions for the calculation of angular displacement and torque of the tunnel, and make the calculation results of cable dynamic tension more secure. The angular displacement of tunnel gradually increases from two sides to the middle, but the torque of tunnel at the anchorage point of the cable is obviously larger than that at other parts. When the cable is subjected to asymmetric load, ignoring the difference between the dynamic tension of cables on both sides will make the calculation result of the cable’s vibration response smaller. Under the seismic load, only odd-order modes participate in the vibration of tunnel, and even-order modes are not excited. When using the mode superposition method, in order to ensure the calculation efficiency and accuracy, it is recommended that the SFT with a span of 500 m or more be calculated with the modal orders above 7, while the SFT below 500 m be calculated with the first 7 modal orders.

     

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