桥梁颤振导数与气动导纳关系的试验验证
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摘要
桥梁断面的气动导纳,除了利用风洞试验直接识别外,Scanlan通过假定Wagner函数和Kussner函数等效提出了利用颤振导数表示的气动导纳关系式,Hatanaka等提出利用"等效"的Theodorsen函数表示的气动导纳。这两种方法虽然简化了气动导纳的识别,但是在逻辑上都存在问题。本文利用风洞试验,识别了平板断面和长宽比为4的矩形断面的颤振导数和气动导纳函数。通过比较识别的气动导纳与利用上述两种方法计算的气动导纳,验证了这两种方法的不合理性。研究结果表明:通过等效的阶跃函数推导的气动导纳函数,因为忽略了高阶运动模式,所以导致识别的气动导纳随着折算频率的增加,与试验直接识别的气动导纳的差距逐渐增大,并最终趋向于一个极限值;这种方法仅在脉动风波长远大于断面特征长度时是适用的;根据等效的Theodorsen函数表示的气动导纳函数,在低频范围内也与直接试验结果较为接近,但是在高频范围内却表现出周期性的波动,而且对于钝体的矩形断面这种波动性更大。这种波动是由于采用了某种等效的Theodorsen函数来描述物体的气动性能,在Theodorsen函数变化后,却保持Theodorsen函数的组成函数维持不变这种逻辑上的错误造成的。
Besides identifying them directly from wind tunnel tests,aerodynamic admittance functions of bridge sections could be expressed using alternative methods. Through assuming Wanger function to be equivalent to Kussner function,Scanlan proposed using bridge flutter derivatives to express aerodynamic admittance functions. Hatanaka et al proposed using ‘equivalent'Theodorsen functions to express aerodynamic admittances. Although both of them simplified identifying aerodynamic admittances,there were logical problems in the two methods. Here,flutter derivatives and aerodynamic admittance functions of a flat plate section and a rectangular section with a aspect ratio of 4 were identified with wind tunnel tests. Then,through comparing the measured aerodynamic admittances with those calculated using the above two methods,irrationality of the two methods was verified. The results indicated that with increase in the reduced frequency,the difference between the calculated aerodynamic admittances using the method of equivalent indicial functions and the measured ones gradually increases and tends to a limit value due to ignoring higher order motion modes,this method is applicable only when the wave length of fluctuating wind is much larger than the characteristic length of bridge sections; the aerodynamic admittances calculated using the equivalent Theodorsen functions are close to the measured ones within a lower frequency range,while they have a periodic fluctuating within a higher frequency range; for rectangular section of bluff bodies,this fluctuating becomes more significant; this fluctuation is due to adopting a certain‘equivalent'Theodorsen function to describe objects' aerodynamic performance,once Theodorsen function changes,but its component functions remain unchanged to cause a logical mistake.
Besides identifying them directly from wind tunnel tests,aerodynamic admittance functions of bridge sections could be expressed using alternative methods. Through assuming Wanger function to be equivalent to Kussner function,Scanlan proposed using bridge flutter derivatives to express aerodynamic admittance functions. Hatanaka et al proposed using ‘equivalent'Theodorsen functions to express aerodynamic admittances. Although both of them simplified identifying aerodynamic admittances,there were logical problems in the two methods. Here,flutter derivatives and aerodynamic admittance functions of a flat plate section and a rectangular section with a aspect ratio of 4 were identified with wind tunnel tests. Then,through comparing the measured aerodynamic admittances with those calculated using the above two methods,irrationality of the two methods was verified. The results indicated that with increase in the reduced frequency,the difference between the calculated aerodynamic admittances using the method of equivalent indicial functions and the measured ones gradually increases and tends to a limit value due to ignoring higher order motion modes,this method is applicable only when the wave length of fluctuating wind is much larger than the characteristic length of bridge sections; the aerodynamic admittances calculated using the equivalent Theodorsen functions are close to the measured ones within a lower frequency range,while they have a periodic fluctuating within a higher frequency range; for rectangular section of bluff bodies,this fluctuating becomes more significant; this fluctuation is due to adopting a certain‘equivalent'Theodorsen function to describe objects' aerodynamic performance,once Theodorsen function changes,but its component functions remain unchanged to cause a logical mistake.
引文
[1]DAVENPORT A G.Buffeting of a suspension bridge by storm winds[J].Journal of the Structural Divion,1962,88(ST3):233-268.
[2]JANCAUSKAS E D,MELBOURNE W H.The aerodynamic admittance of two-dimensional rectangular section cylinders in smooth flow[J].Journal of Wind Engineering and Industrial Aerodynamics,1986,23(1/2/3):395-408.
[3]SANKARAN R,JANCAUSKAS E D.Direct measurement of the aerodynamic admittance of two-dimensional rectangular cylinders in smooth and turbulent flows[J].Journal of Wind Engineering and Industrial Aerodynamics,1992,41(1/2/3):601-611.
[4]潘韬,赵林,曹曙阳,等.多风扇主动控制风洞类平板断面抖振力识别研究[J].振动与冲击,2010,29(6):178-183.PAN Tao,ZHAO Lin,CAO Shuyang,et al.Buffeting force analysis of thin plate section in multiple fan active control wind tunnel[J].Journal of Vibration and Shock,2010,29(6):178-183.
[5]周奇,朱乐东,任鹏杰,等.气动干扰对平行双幅断面气动导纳影响研究[J].振动与冲击,2014,33(14):125-131.ZHOU Qi,ZHU Ledong,REN Pengjie,et al.Aerodynamic interfere effect on the aerodynamic admittance of paralleled double girders[J].Journal of Vibration and Shock,2014,33(14):125-131.
[6]SCANLAN R H.Problematics in formulation of wind-force models for bridge decks[J].Journal of Engineering Mechanics,1993,119(7):1353-1375.
[7]SCANLAN R H.Motion-related body-force functions in twodimensional low-speed flow[J].Journal of Fluids and Structures,2000,14(1):49-63.
[8]SCANLAN R H.Reexamination of sectional aerodynamic force functions for bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,2001,89(14/15):1257-1266.
[9]SCANLAN R H,JONES N P.A form of aerodynamic admittance for use in bridge aeroelastic analysis[J].Journal of Fluids and Structures,1999,13(7/8):1017-1027.
[10]TUBINO F.Relationships among aerodynamic admittance functions,flutter derivatives and static coefficients for longspan bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,2005,93(12):929-950.
[11]HATANAKA A,TANAKA H.New estimation method of aerodynamic admittance function[J].Journal of Wind Engineering and Industrial Aerodynamics,2002,90(12/13/14/15):2073-2086.
[12]HATANAKA A,TANAKA H.Aerodynamic admittance functions of rectangular cylinders[J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6/7):945-953.
[13]COSTA C.Aerodynamic admittance functions and buffeting forces for bridges via Indicial functions[J].Journal of Fluids and Structures,2007,23(3):413-428.
[14]王雄江,顾明,翟伟廉.桥梁气动导纳识别的阶跃函数你合法[J].土木工程学报,2011,44(11):66-73.WANG Xiongjiang,GU Ming,ZHAI Weilian.Determinant of aerodynamic admittance functions of bridge deck by using indicial functions[J].China Civil Engineering Journal,2011,44(11):66-73.
[15]张志田,陈政清.桥梁断面几种气动导纳模型的合理性剖析[J].土木工程学报,2012,45(8):104-113.ZHANG Zhitian,CHEN Zhengqing.Rationality analysis of some existing aerodynamic admittance models for bridge deck sections[J].China Civil Engineering Journal,2012,45(8):104-113.
[16]ZHANG Z T,GE Y J,ZHANG W F.Superposability of unsteady aerodynamic loads on bridge deck sections[J].Journal of Central South University,2013,20(11):3202-3215.
[17]SCANLAN R H,TOMKO J J.Airfoil and bridge deck flutter derivatives[J].Journal of the Engineering Mechanics Division,1971,97(6):1717-1737.
[18]GARRICK I.On some reciprocal relations in the theory of nonstationary flows[R].NACA Report 629,1938.
[19]THEODORSEN T.General theory of aerodynamic instability and the mechanism of flutter[R].NACA Report 496,1949.
[20]陈政清,胡建华.桥梁颤振导数识别的时域法与频域法对比研究[J].工程力学,2005,22(6):127-133.CHEN Zhengqing,HU Jianhua.A comparative study between time-domain method and frequency-domain method for identification of bridge flutter derivatives[J].Engineering Mechanics,2005,22(6):127-133.
[21]MATSUMOTO M,YAGI T,TAMAKI H,et al.Vortexinduced vibration and its effect on torsional flutter instability in the case of B/D=4 rectangular cylinder[J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6/7):971-983.
[22]NIETO F,HARGREAVES D M,OWEN J S.On the applicability of 2D URANS and SST k-ωturbulence model to the fluid-structure interaction of rectangular cylinders[J].Engineering Application of Computational Fluid Mechanics,2015,9(1):157-173.
[23]LAROSE G L.Experimental determination of the aerodynamic admittance of a bridge deck segment[J].Journal of Fluids and Structures,1999,13(7):1029-1040.
[23]靳新华.桥梁断面气动导纳识别理论及试验研究[D].上海:同济大学,2003.
[24]徐自然,周奇,朱乐东.考虑模型抖振力跨向不完全相关性效应的气动导纳识别[J].实验流体力学,2014,28(5):39-46.XU Ziran,ZHOU Qi,ZHU Ledong.Identification of aerodynamic admittances by considering the effect of incomplete span-wise correlation of buffeting forces on section model[J].Journal of Experiments in Fluid Mechanics,2014,28(5):39-46.
[2]JANCAUSKAS E D,MELBOURNE W H.The aerodynamic admittance of two-dimensional rectangular section cylinders in smooth flow[J].Journal of Wind Engineering and Industrial Aerodynamics,1986,23(1/2/3):395-408.
[3]SANKARAN R,JANCAUSKAS E D.Direct measurement of the aerodynamic admittance of two-dimensional rectangular cylinders in smooth and turbulent flows[J].Journal of Wind Engineering and Industrial Aerodynamics,1992,41(1/2/3):601-611.
[4]潘韬,赵林,曹曙阳,等.多风扇主动控制风洞类平板断面抖振力识别研究[J].振动与冲击,2010,29(6):178-183.PAN Tao,ZHAO Lin,CAO Shuyang,et al.Buffeting force analysis of thin plate section in multiple fan active control wind tunnel[J].Journal of Vibration and Shock,2010,29(6):178-183.
[5]周奇,朱乐东,任鹏杰,等.气动干扰对平行双幅断面气动导纳影响研究[J].振动与冲击,2014,33(14):125-131.ZHOU Qi,ZHU Ledong,REN Pengjie,et al.Aerodynamic interfere effect on the aerodynamic admittance of paralleled double girders[J].Journal of Vibration and Shock,2014,33(14):125-131.
[6]SCANLAN R H.Problematics in formulation of wind-force models for bridge decks[J].Journal of Engineering Mechanics,1993,119(7):1353-1375.
[7]SCANLAN R H.Motion-related body-force functions in twodimensional low-speed flow[J].Journal of Fluids and Structures,2000,14(1):49-63.
[8]SCANLAN R H.Reexamination of sectional aerodynamic force functions for bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,2001,89(14/15):1257-1266.
[9]SCANLAN R H,JONES N P.A form of aerodynamic admittance for use in bridge aeroelastic analysis[J].Journal of Fluids and Structures,1999,13(7/8):1017-1027.
[10]TUBINO F.Relationships among aerodynamic admittance functions,flutter derivatives and static coefficients for longspan bridges[J].Journal of Wind Engineering and Industrial Aerodynamics,2005,93(12):929-950.
[11]HATANAKA A,TANAKA H.New estimation method of aerodynamic admittance function[J].Journal of Wind Engineering and Industrial Aerodynamics,2002,90(12/13/14/15):2073-2086.
[12]HATANAKA A,TANAKA H.Aerodynamic admittance functions of rectangular cylinders[J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6/7):945-953.
[13]COSTA C.Aerodynamic admittance functions and buffeting forces for bridges via Indicial functions[J].Journal of Fluids and Structures,2007,23(3):413-428.
[14]王雄江,顾明,翟伟廉.桥梁气动导纳识别的阶跃函数你合法[J].土木工程学报,2011,44(11):66-73.WANG Xiongjiang,GU Ming,ZHAI Weilian.Determinant of aerodynamic admittance functions of bridge deck by using indicial functions[J].China Civil Engineering Journal,2011,44(11):66-73.
[15]张志田,陈政清.桥梁断面几种气动导纳模型的合理性剖析[J].土木工程学报,2012,45(8):104-113.ZHANG Zhitian,CHEN Zhengqing.Rationality analysis of some existing aerodynamic admittance models for bridge deck sections[J].China Civil Engineering Journal,2012,45(8):104-113.
[16]ZHANG Z T,GE Y J,ZHANG W F.Superposability of unsteady aerodynamic loads on bridge deck sections[J].Journal of Central South University,2013,20(11):3202-3215.
[17]SCANLAN R H,TOMKO J J.Airfoil and bridge deck flutter derivatives[J].Journal of the Engineering Mechanics Division,1971,97(6):1717-1737.
[18]GARRICK I.On some reciprocal relations in the theory of nonstationary flows[R].NACA Report 629,1938.
[19]THEODORSEN T.General theory of aerodynamic instability and the mechanism of flutter[R].NACA Report 496,1949.
[20]陈政清,胡建华.桥梁颤振导数识别的时域法与频域法对比研究[J].工程力学,2005,22(6):127-133.CHEN Zhengqing,HU Jianhua.A comparative study between time-domain method and frequency-domain method for identification of bridge flutter derivatives[J].Engineering Mechanics,2005,22(6):127-133.
[21]MATSUMOTO M,YAGI T,TAMAKI H,et al.Vortexinduced vibration and its effect on torsional flutter instability in the case of B/D=4 rectangular cylinder[J].Journal of Wind Engineering and Industrial Aerodynamics,2008,96(6/7):971-983.
[22]NIETO F,HARGREAVES D M,OWEN J S.On the applicability of 2D URANS and SST k-ωturbulence model to the fluid-structure interaction of rectangular cylinders[J].Engineering Application of Computational Fluid Mechanics,2015,9(1):157-173.
[23]LAROSE G L.Experimental determination of the aerodynamic admittance of a bridge deck segment[J].Journal of Fluids and Structures,1999,13(7):1029-1040.
[23]靳新华.桥梁断面气动导纳识别理论及试验研究[D].上海:同济大学,2003.
[24]徐自然,周奇,朱乐东.考虑模型抖振力跨向不完全相关性效应的气动导纳识别[J].实验流体力学,2014,28(5):39-46.XU Ziran,ZHOU Qi,ZHU Ledong.Identification of aerodynamic admittances by considering the effect of incomplete span-wise correlation of buffeting forces on section model[J].Journal of Experiments in Fluid Mechanics,2014,28(5):39-46.