﻿ 均匀流作用下悬浮隧道的涡激振动响应 Vortex-Induced Vibration Response of Submerged Floating Tunnel (SFT) under Uniform Flow

International Journal of Mechanics Research
Vol.03 No.01(2014), Article ID:13591,11 pages
10.12677/IJM.2014.31001

Vortex-Induced Vibration Response of Submerged Floating Tunnel (SFT) under Uniform Flow

Mansheng Dong, Longchang Yang

School of Transportation Engineering, Hefei University of Technology, Hefei

Email: dongmans@sina.com

Received: Apr. 5th, 2014; revised: May 5th, 2014; accepted: May 12th, 2014

ABSTRACT

In order to analyze the dynamic response of submerged floating tunnel (SFT) in uniform flows under vortex-induced vibration (VIV), equations of motion control of SFT were derived by simplifying SFT as a beam with elastic bearings. The analytical solution was presented by using the Galerkin method and the modal superposition method. The displacement curves of SFT at the intermediate span were gained by using Matlab. The nonlinear vibration characteristics about SFT were analyzed. The results show that both damping and spring of the elastic bearings have a role in reducing the response displacement of SFT, while the effect of stiffness of spring on the SFT is greater than that of damping coefficient.

Keywords:Submerged Floating Tunnel, Vortex-Induced Vibration, Dynamic Response, Elastic Beam, Galerkin Method

Email: dongmans@sina.com

1. 引言

2. 均匀流中涡激振动作用下悬浮隧道的模型

2.1. 悬浮隧道的物理模型

Figure 1. Schematic diagram of SFT model

Figure 2. Schematic cross section of SFT on the tension leg

Figure 3. Schematic diagram of SFT simplified physical model

Figure 4. Schematic diagram of SFT simplified physical model on the tension leg

1) 悬浮隧道跨中的张力腿被简化成两端支座处的弹簧；

2) 被简化的两端支座处的弹簧的竖向刚度为K，它的质量所占悬浮隧道整体结构的质量比例很小，可以忽略不计；

3) 悬浮隧道的弹性支座的阻尼系数为c1，同样它的质量也可以忽略不计；

4) 对于处在均匀流中的涡激振动下的悬浮隧道，只考虑它的一阶模态，其他的高阶模态在不很大影响最终计算结果的基础上予以忽略[10] 。

2.2. 悬浮隧道的动力平衡方程

(1)

(2)

(3)

(4)

2.3. 悬浮隧道的边界条件

(5)

Figure 5. Calculation model of SFT

2.4. 悬浮隧道的动力平衡方程的求解

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

3. 悬浮隧道动力响应的模拟结果

3.1. 悬浮隧道的参数

3.2. 模拟的结果

Figure 6. Design cross-section of SFT

Figure 7. Dynamic response of SFTwhen c1 = 3500 N/(m/s)

Table 1. Thebasic parameters of SFT

Figure 8. Dynamic response of SFT when c1 = 10,000 N/(m/s)

Figure 9. Dynamic response of SFT when c1 = 20,000 N/(m/s)

Figure 10. Dynamic response of SFT when c1 = 50,000 N/(m/s)

Figure 11. Dynamic response of SFT when K = 1000 N/m

Figure 12. Dynamic response of SFT when K = 3000 N/m

Figure 13. Dynamic response of SFT when K = 5000 N/m

N/(m/s)，c1 = 10,000 N/(m/s)，c1 = 20,000 N/(m/s)和c1 = 50,000 N/(m/s)时，悬浮隧道跨中的位移的幅值随K值的增加而减小明显。当c1 = 3500 N/(m/s)和c1 = 10,000 N/(m/s)时，悬浮隧道跨中位移的幅值随着K值由1000 N/m增加到3000 N/m而由0.4 m降到0.15 m；当c1 = 20,000 N/(m/s)时，悬浮隧道跨中位移的幅值随着K值由1000 N/m增加到3000 N/m而由0.25 m降到0.15 m；当c1 = 50,000 N/(m/s)时，悬浮隧道跨中部的位移的幅值随着K值由1000 N/m增加到3000 N/m而由0.3 m降到0.15 m。当c1 = 20,000 N/(m/s)时，其他条件相同时，悬浮隧道的跨中位移幅值最小。

4. 结论

1) 悬浮隧道弹性支撑的阻尼c1对减小悬浮隧道跨中的位移幅值有微小作用。随着阻尼的增加，悬浮隧道跨中位移总体上几乎保持不变。只有当K值相对较小时，悬浮隧道跨中位移才会随着c1值的增加而减小。同时，c1值对悬浮隧道的影响随着K值的增大而降低。

2) 悬浮隧道两端弹性支撑的弹簧对降低悬浮隧道跨中位移的幅值有明显作用，跨中位移的幅值随着弹簧刚度K值的增大而明显降低。

3) 从上可知，在降低悬浮隧道跨中位移幅值的问题上，弹性支撑的弹簧比阻尼拥有明显的作用。

Vortex-Induced Vibration Response of Submerged Floating Tunnel (SFT) under Uniform Flow. 力学研究,01,1-12. doi: 10.12677/IJM.2014.31001

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