THE WIND-INDUCED VIBRATION CONTROL OF HIGH-RISE CHIMNEYS BY A TUNED MASS DAMPER INERTER (TMDI)
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摘要: 高耸烟囱是一种典型的风敏感结构，尤其是横风向涡激共振会对结构安全造成不利影响，往往需要对其进行风振控制。相比传统的调谐质量阻尼器(TMD)，调谐质量惯容阻尼器(TMDI)能够通过惯容器实现动力吸振器的轻量化设计。但惯容器的连接位置，不仅影响其在对高耸烟囱结构上实施的难度，对风振控制效果的影响也尚待定量化研究。该文将高耸烟囱简化为广义单自由度结构，基于风荷载频谱的滤波表示，推导了TMDI控制下结构风振响应的解析解。在此基础上，对TMDI最优设计参数进行了参数化分析，总结了相应的经验公式供设计参考。此外，通过对比TMDI与TMD的风振响应控制效果，给出了惯容器起增强控制效果的判别准则，以及TMDI的等效TMD质量比计算公式，以指导动力吸振器的轻量化设计。最后，通过对某270 m高混凝土烟囱风洞试验数据进行TMDI风振控制算例分析，验证了理论分析的有效性。结果表明，采用该文优化设计方法，TMDI可降低涡激共振锁定区内高耸烟囱的设计风荷载45%以上。Abstract: The high-rise chimney is a typical wind-sensitive structure. The crosswind vortex-induced resonance will have an adverse impact on the structural safety. Compared with traditional tuned mass dampers (TMDs), the tuned mass damper inerter (TMDI) can realize the lightweight design of the dynamic vibration absorber via the massless inerter. However, the location of the inerter affects not only its implementation on the high-rise chimney structure, but also the vibration control performance, which requires detailed quantitative studies. A high-rise chimney is simplified as a generalized single degree of freedom structure. Based on the analog filter representation of wind load spectra, the analytical solution of wind-induced response of the structure under TMDI control is derived. Subsequently, a parametric analysis of TMDI optimal design parameters is performed. Corresponding empirical formulas are summarized for design reference. In addition, by comparing the control effect of TMDI and TMD, the criterion of enhancing the control effect of inerter and the formula of equivalent TMD mass ratio of the TMDI are given to guide the lightweight design of the dynamic vibration absorbers. Finally, the effectiveness of the theoretical analysis is validated by a numerical TMDI control example based on the wind tunnel test data of a concrete chimney of 270 m tall. The results show that TMDI can reduce the design wind load of high-rise chimney by more than 45% in the vortex induced resonance lock-in region.
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Key words:
- high-rise structure /
- tuned mass damper inerter /
- wind-induced response /
- chimney /
- vibration control
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图 4 典型工况下Jw(虚线)、Ja(实线)、Jc(点划线)随ν和ζd变化的等值线图(μ = 1%，ζs = 1%)
Figure 4. Contours of Jw (dash line), Ja (solid line) and Jc (dot dash line) with respect to ν and ζd under typical cases (μ = 1%, ζs = 1%)
图 5 最优控制参数(νopt，ζdopt)和最优控制比Jopt随惯容器参数(β，φ)的变化(μ = 1%，ζs = 1%)
Figure 5. Optimal parameter (νopt, ζdopt) optimal control ratio Jopt with respect to inerter parameter (β, φ) (μ = 1%, ζs = 1%)
图 6 采用最优控制参数(νopt，ζdopt)经验公式得到的最优控制比Jopt与分析结果的对比
Figure 6. Comparisons of Jopt results estimated by empirical formula of optimal parameter (νopt, ζdopt) with parametric analysis results
图 7 惯容器影响系数R随惯容器参数(β，φ)的变化(μ = 1%)
Figure 7. Inerter influence factor R with inerter parameters (β, φ) with μ = 1%
图 8 不同质量比μ下的惯容器增强区边界线
Figure 8. Inerter enhancement boundary lines under different mass ratios μ
图 9 惯容器影响系数R随判别参数β·(1 – φ)2 / μ的变化
Figure 9. Inerter influence factor R with respect to β·(1–φ)2/μ
图 10 惯容增强区判别准则的假设检验
Figure 10. Hypothesis test on creation of inerter enhancement region
图 12 惯容影响系数R的经验公式与分析结果对比
Figure 12. Comparison between empirical formula and analysis results of inerter influence factor R
图 14 气弹模型风洞试验得到的气动阻尼比随风速的变化
Figure 14. Aerodynamic damping ratio with respect to wind speed obtained by wind tunnel tests on an aeroelastic model
图 15 不同控制工况下的烟囱脉动风振响应均方根
Figure 15. Root of mean square values of wind-induced responses on chimney under different control cases
图 16 典型控制工况TMDI与等效TMD横风向共振响应时程对比(U/UCr = 1.17)
Figure 16. Comparisons of time histories of resonant cross-wind responses controlled by TMDI and equivalent TMD under typical cases (U/UCr = 1.17)
图 17 不同设计风速下的最不利风振响应
Figure 17. Most unfavorable wind-induced responses under different design wind speeds
图 18 不同设计风速下的最不利风振响应控制率
Figure 18. Control rates of most unfavorable wind-induced responses under different design wind speeds
表 1 风振控制计算工况阻尼器详细参数
Table 1. Detailed damper parameters of wind-induced vibration control cases
工况号参数 1 2 3 4 5 μ/(%) 1.000 1.000 1.000 1.000 1.000 β/(%) 0.000 20.000 20.000 20.000 20.000 φ − 0.900 0.750 0.500 0.000 ν 0.990 0.993 0.983 0.947 0.826 ζd/(%) 4.975 3.827 6.505 11.490 20.830 m/t 45.880 45.880 45.880 45.880 45.880 c/(kN·s/m) 11.210 181.700 305.600 520.200 822.900 k/(kN/m) 276.800 5848.100 5726.800 5319.300 4049.900 b/(kN·s2/m) 0.000 917.600 917.600 917.600 917.600 χ/m − 256 233 193 0 μe/(%) 1.0 − 2.25 6.0 21.0 
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表 2 典型风速下风振响应计算结果及误差
Table 2. Results and errors of wind-induced responses under typical wind speed cases
工况 U/UCr 方法 顺风向 横风向 σxa/D/(%) 误差/(%) σxc/D/(%) 误差/(%) 未控制 0.68 气弹试验 0.044 − 0.090 − 时域分析 0.045 2.0 0.095 5.9 本文方法 0.047 6.2 0.097 8.2 1.17 气弹试验 0.122 − 0.460 − 时域分析 0.125 2.3 0.474 3.1 本文方法 0.127 3.9 0.475 3.3 2.63 气弹试验 0.822 − 0.760 − 时域分析 0.827 0.6 0.762 0.2 本文方法 0.841 2.3 0.777 2.1 控制工况1 0.68 时域分析 0.032 − 0.070 − 本文方法 0.032 1.2 0.075 7.8 1.17 时域分析 0.084 − 0.326 − 本文方法 0.087 3.4 0.317 −2.8 2.63 时域分析 0.542 − 0.596 − 本文方法 0.545 0.5 0.597 0.2 控制工况2 0.68 时域分析 0.035 − 0.076 − 本文方法 0.035 1.5 0.083 8.7 1.17 时域分析 0.093 − 0.365 − 本文方法 0.097 3.5 0.355 −2.9 2.63 时域分析 0.613 − 0.651 − 本文方法 0.617 0.5 0.653 0.2 控制工况3 0.68 时域分析 0.030 − 0.065 − 本文方法 0.030 1.0 0.070 7.2 1.17 时域分析 0.078 − 0.300 − 本文方法 0.080 2.1 0.291 −2.7 2.63 时域分析 0.499 − 0.555 − 本文方法 0.502 0.5 0.556 0.2 控制工况4 0.68 时域分析 0.026 − 0.054 − 本文方法 0.027 0.4 0.057 6.2 1.17 时域分析 0.067 − 0.240 − 本文方法 0.069 2.9 0.234 −2.6 2.63 时域分析 0.408 − 0.458 − 本文方法 0.410 0.5 0.459 0.2 控制工况5 0.68 时域分析 0.024 − 0.042 − 本文方法 0.024 −0.3 0.044 5.5 1.17 时域分析 0.057 − 0.184 − 本文方法 0.059 2.7 0.179 −2.6 2.63 时域分析 0.329 − 0.357 − 本文方法 0.331 0.4 0.357 0.2
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