空间网壳结构的节点-构件阻尼模型研究
|
摘要
目前尽管对已有的阻尼模型进行了大量研究,然而,经典黏性阻尼模型会过高估计阻尼力,无法真实地描述结构内未知的非线性的能量耗散,而非黏性阻尼模型应用于工程实践还存在诸多问题。针对网壳结构中的阻尼源,提出一种节点-构件阻尼模型,在节点处考虑节点与构件之间的摩擦阻尼效应,而构件的材料阻尼则认为与应力水平有关。以单层大跨空间网壳为例,对地震荷载作用下网壳结构的材料阻尼比进行评价,研究了不同阻尼模型对结构动力需求的影响。研究表明:1当材料能量耗散公式中的指数n取2.4时,该结构的平均材料阻尼比大约为0.45%~0.5%;2不同阻尼模型对网壳结构的动力需求、稳定性等参数影响显著,合适的阻尼模型的选择是对结构进行合理的抗震性能评估的前提条件,然而,在工程结构的动力分析中,这一事实往往被忽视;3提出的节点-构件阻尼模型的能量耗散主要依赖于材料的塑形变形能,从而在一定程度上消除了Rayleigh阻尼模型会过高估计结构内黏性阻尼力的缺陷。提出的这种阻尼模型,也可应用于其他形式的建筑结构体系(如平面网架)和建筑结构具有非比例黏性阻尼的情况。
At present the existing viscous damping models have been investigated by many researchers,while the damping force of a structure will be overestimated when these classical models are used in dynamic analyses,thus the nonlinear energy dissipation mechanism of the structure cannot be well described. Furthermore,there are many problems when the non-viscous damping models are applied in engineering practice. Aiming at the damping sources in single-layer latticed domes,a joint-member damping model is proposed,in which the friction damping effects at the joint are taken into account and the material damping is considered to be stress-dependent. Taking the single-layer latticed dome as the example,the structural material damping ratios are evaluated and the effects of the different damping models on the dynamic demands of the structure subjected to seismic ground motions are investigated. It shows that 1 the equivalent structural material damping ratio is about 0. 45% ~ 0. 5% when the exponent in the formula for material energy dissipation is taken to be 2. 4; 2 the damping models have significant effects on the dynamic demands and stability of a structure,and an appropriate damping model is critical for reasonably evaluating the seismic performance of a structure,which has not been well recognized in engineering practice; 3 the energy dissipation in the joint-element damping model depends heavily on the plastic deformation energy,thus to some certain extension,it can eliminate effects of the unrealistic high damping forces due to the adoption of the Rayleigh damping model. The damping model proposed in this paper can also be applied to other structural systems,e. g. flat grid structures and structures with non-proportional viscous damping.
At present the existing viscous damping models have been investigated by many researchers,while the damping force of a structure will be overestimated when these classical models are used in dynamic analyses,thus the nonlinear energy dissipation mechanism of the structure cannot be well described. Furthermore,there are many problems when the non-viscous damping models are applied in engineering practice. Aiming at the damping sources in single-layer latticed domes,a joint-member damping model is proposed,in which the friction damping effects at the joint are taken into account and the material damping is considered to be stress-dependent. Taking the single-layer latticed dome as the example,the structural material damping ratios are evaluated and the effects of the different damping models on the dynamic demands of the structure subjected to seismic ground motions are investigated. It shows that 1 the equivalent structural material damping ratio is about 0. 45% ~ 0. 5% when the exponent in the formula for material energy dissipation is taken to be 2. 4; 2 the damping models have significant effects on the dynamic demands and stability of a structure,and an appropriate damping model is critical for reasonably evaluating the seismic performance of a structure,which has not been well recognized in engineering practice; 3 the energy dissipation in the joint-element damping model depends heavily on the plastic deformation energy,thus to some certain extension,it can eliminate effects of the unrealistic high damping forces due to the adoption of the Rayleigh damping model. The damping model proposed in this paper can also be applied to other structural systems,e. g. flat grid structures and structures with non-proportional viscous damping.
引文
[1]Adhikari S.Dynamics of nonviscously damped linear systems[J].Journal of Engineering Mechanics,2002,128(3):328-339
[2]Woodhouse J.Linear damping models for structural vibration[J].Journal of Sound and Vibration,1998,215(3):547-569
[3]Zhang H,Han Q.A numerical investigation of seismic performance of large span single-layer latticed domes with semi-rigid joints[J].Structural Engineering and Mechanics,2013,48(1):57-75
[4]Bathe K J.Finite element procedures[M].New Jersey:Prentice Hall,1996
[5]NIST GCR 10-917-5.Nonlinear structural analysis for seismic design:A guide for practicing engineers[S].National Institute of Standards and Technology(NIST),2010
[6]Hall J F.Problems encountered from the use(or misuse)of Rayleigh damping[J].Earthquake Engineering and Structural Dynamics,2006,35(5):525-545
[7]Kijewski-Correa T,Pirnia J D.Dynamic behavior of tall buildings under wind:insights from full‐scale monitoring[J].The Structural Design of Tall and Special Buildings,2007,16(4):471-486
[8]Wu J R,Liu P F,Li Q S.Effects of amplitude-dependent damping and time constant on wind-induced responses of super tall building[J].Computers&Structures,2007,85(15):1165-1176
[9]Chopra A K.Dynamics of structures:theory and applications to earthquake engineering[M].New Jersey:Prentice Hall,1995
[10]Val D V,Segal F.Effect of damping model on pre-yielding earthquake response of structures[J].Engineering Structures,2005,27(14):1968-1980
[11]Adhikari S.Damping modelling using generalized proportional damping[J].Journal of Sound and Vibration,2006,293(1):156-170
[12]Charney F A.Unintended consequences of modeling damping in structures[J].Journal of Structural Engineering,2008,134(4):581-592
[13]Bernal D.Viscous damping in inelastic structural response[J].Journal of Structural Engineering,1994,120(4):1240-1254
[14]Bruneau M,Uang C M,sabelli R.Ductile design of steel structures[M].2nd Edition.New York:Mc Graw-Hill Professional,2011
[15]GB 50011—2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010(GB 50011—2010 Code for seismic design of buildings[S].Beijing:China Architecture&Building Press,2010(in Chinese))
[16]ASCE/SEI 7-10.Minimum design loads for buildings and other structures[S].Reston,Virginia:American Society of Civil Engineers,2010
[17]PEER/ATC 72-1.Modeling and acceptance criteria for seismic design and analysis of tall buildings[S].Redwood City:Applied Technology Council,2010
[18]ANSI/AISC 341-05.Seismic provisions for structural steel buildings[S].Chicago,Illinois:American Institute of Steel Construction,2005
[19]Ahmadi Asoor A A,Pashaei M H.Experimentally study on the effects of type of joint on damping[J].World Applied Sciences Journal,2010,8(5):608-613
[20]Priestley M J N,Grant D N.Viscous damping in seismic design and analysis[J].Journal of Earthquake Engineering,2005,9(S2):229-255
[21]应怀樵,刘进明,沈松.半功率带宽法与INV阻尼计法求阻尼比的研究[J].噪声与振动控制,2006,26(2):4-6(Ying Huaiqiao,Liu Jinming,Shen Song.Half-power bandwidth method and INV damping ration solver study[J].Noise and Vibration Control,2006,26(2):4-6(in Chinese))
[22]Goodman L E.Material damping and slip damping[M]//Shock and Vibration Handbook.5th Edition.New York:Mc Graw-Hill,2002
[23]Gounaris G D,Anifantis N K.Structural damping determination by finite element approach[J].Computers and Structures,1999,73(1):445-452
[24]Gounaris G D,Antonakakis E,Papadopoulos C A.Hysteretic damping of structures vibrating at resonance:An iterative complex eigensolution method based on damping-stress relation[J].Computers&Structures,2007,85(23):1858-1868
[25]Ting J M,Crawley F.Characterization of damping of materials and structures from nanostrain levels to one thousand microstrain[J].AIAA Journal,1992,30(7):1856-1863
[26]Maedel Jr P.Vibration standards and test codes[M]//Shock and Vibration Handbook.5th Edition.New York:Mc Graw-Hill,2002
[27]Beards C F.Structural vibration analysis and damping[M].Oxford:Butterworth-Heinemann,1996
[28]Clarence W S.Vibration and shock handbook[M].CRC Press,Taylor&Francis Group,2005
[29]Zhang H D,Wang Y F,Han Q H.Nonlinear material loss factors of single-layer latticed domes subjected to earthquake ground motions[J].Journal of Structural Engineering,2014.Doi:10.1061/(ASCE)ST.1943-541X.0001149,04014181
[30]Bingham J G,Crookston J R,Dutson J D,et al.The joint damping experiment(JDX)[M].National Aeronautics and Space Administration,Langley Research Center,1997
[31]Gaul L,Nitsche R.The role of friction in mechanical joints[J].Applied Mechanics Reviews,2001,54(2):93-106
[32]李庆祥,王东生,李玉和.现代精密仪器设计[M].北京:清华大学出版社,2004(Li Qingxiang,Wang Dongsheng,Li Yuhe.Design of modern precision instruments[M].Beijing:Tsinghua University Press,2004(in Chinese))
[33]Zareian F,Medina R A.A practical method for proper modeling of structural damping in inelastic plane structural systems[J].Computers&Structures,2010,88(1):45-53
[34]Lin Y Y,Miranda E,Chang K C.Evaluation of damping reduction factors for estimating elastic response of structures with high damping[J].Earthquake Engineering&Structural Dynamics,2005,34(11):1427-1443
[35]Li Q S,Fang J Q,Jeary A P.Free vibration analysis of cantilevered tall structures under various axial loads[J].Engineering Structures,2000,22(5):525-534
[36]张辉东,王元丰,江辉.不同参数取值对复阻尼模型结构抗震性能的影响[J].建筑结构学报,2009,30(6):94-100(Zhang Huidong,Wang Yuanfeng,Jiang Hui.Effect of different parameters on seismic performance of complex damping structures[J].Journal of Building Structures,2009,30(6):94-100(in Chinese))
[37]Erduran E.Evaluation of Rayleigh damping and its influence on engineering demand parameter estimates[J].Earthquake Engineering&Structural Dynamics,2012,41(14):1905-1919
[38]Pant D R,Wijeyewickrema A C,El Gawady M A.Appropriate viscous damping for nonlinear time-history analysis of baseisolated reinforced concrete buildings[J].Earthquake Engineering&Structural Dynamics,2013,42(15):2321-2339
[2]Woodhouse J.Linear damping models for structural vibration[J].Journal of Sound and Vibration,1998,215(3):547-569
[3]Zhang H,Han Q.A numerical investigation of seismic performance of large span single-layer latticed domes with semi-rigid joints[J].Structural Engineering and Mechanics,2013,48(1):57-75
[4]Bathe K J.Finite element procedures[M].New Jersey:Prentice Hall,1996
[5]NIST GCR 10-917-5.Nonlinear structural analysis for seismic design:A guide for practicing engineers[S].National Institute of Standards and Technology(NIST),2010
[6]Hall J F.Problems encountered from the use(or misuse)of Rayleigh damping[J].Earthquake Engineering and Structural Dynamics,2006,35(5):525-545
[7]Kijewski-Correa T,Pirnia J D.Dynamic behavior of tall buildings under wind:insights from full‐scale monitoring[J].The Structural Design of Tall and Special Buildings,2007,16(4):471-486
[8]Wu J R,Liu P F,Li Q S.Effects of amplitude-dependent damping and time constant on wind-induced responses of super tall building[J].Computers&Structures,2007,85(15):1165-1176
[9]Chopra A K.Dynamics of structures:theory and applications to earthquake engineering[M].New Jersey:Prentice Hall,1995
[10]Val D V,Segal F.Effect of damping model on pre-yielding earthquake response of structures[J].Engineering Structures,2005,27(14):1968-1980
[11]Adhikari S.Damping modelling using generalized proportional damping[J].Journal of Sound and Vibration,2006,293(1):156-170
[12]Charney F A.Unintended consequences of modeling damping in structures[J].Journal of Structural Engineering,2008,134(4):581-592
[13]Bernal D.Viscous damping in inelastic structural response[J].Journal of Structural Engineering,1994,120(4):1240-1254
[14]Bruneau M,Uang C M,sabelli R.Ductile design of steel structures[M].2nd Edition.New York:Mc Graw-Hill Professional,2011
[15]GB 50011—2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010(GB 50011—2010 Code for seismic design of buildings[S].Beijing:China Architecture&Building Press,2010(in Chinese))
[16]ASCE/SEI 7-10.Minimum design loads for buildings and other structures[S].Reston,Virginia:American Society of Civil Engineers,2010
[17]PEER/ATC 72-1.Modeling and acceptance criteria for seismic design and analysis of tall buildings[S].Redwood City:Applied Technology Council,2010
[18]ANSI/AISC 341-05.Seismic provisions for structural steel buildings[S].Chicago,Illinois:American Institute of Steel Construction,2005
[19]Ahmadi Asoor A A,Pashaei M H.Experimentally study on the effects of type of joint on damping[J].World Applied Sciences Journal,2010,8(5):608-613
[20]Priestley M J N,Grant D N.Viscous damping in seismic design and analysis[J].Journal of Earthquake Engineering,2005,9(S2):229-255
[21]应怀樵,刘进明,沈松.半功率带宽法与INV阻尼计法求阻尼比的研究[J].噪声与振动控制,2006,26(2):4-6(Ying Huaiqiao,Liu Jinming,Shen Song.Half-power bandwidth method and INV damping ration solver study[J].Noise and Vibration Control,2006,26(2):4-6(in Chinese))
[22]Goodman L E.Material damping and slip damping[M]//Shock and Vibration Handbook.5th Edition.New York:Mc Graw-Hill,2002
[23]Gounaris G D,Anifantis N K.Structural damping determination by finite element approach[J].Computers and Structures,1999,73(1):445-452
[24]Gounaris G D,Antonakakis E,Papadopoulos C A.Hysteretic damping of structures vibrating at resonance:An iterative complex eigensolution method based on damping-stress relation[J].Computers&Structures,2007,85(23):1858-1868
[25]Ting J M,Crawley F.Characterization of damping of materials and structures from nanostrain levels to one thousand microstrain[J].AIAA Journal,1992,30(7):1856-1863
[26]Maedel Jr P.Vibration standards and test codes[M]//Shock and Vibration Handbook.5th Edition.New York:Mc Graw-Hill,2002
[27]Beards C F.Structural vibration analysis and damping[M].Oxford:Butterworth-Heinemann,1996
[28]Clarence W S.Vibration and shock handbook[M].CRC Press,Taylor&Francis Group,2005
[29]Zhang H D,Wang Y F,Han Q H.Nonlinear material loss factors of single-layer latticed domes subjected to earthquake ground motions[J].Journal of Structural Engineering,2014.Doi:10.1061/(ASCE)ST.1943-541X.0001149,04014181
[30]Bingham J G,Crookston J R,Dutson J D,et al.The joint damping experiment(JDX)[M].National Aeronautics and Space Administration,Langley Research Center,1997
[31]Gaul L,Nitsche R.The role of friction in mechanical joints[J].Applied Mechanics Reviews,2001,54(2):93-106
[32]李庆祥,王东生,李玉和.现代精密仪器设计[M].北京:清华大学出版社,2004(Li Qingxiang,Wang Dongsheng,Li Yuhe.Design of modern precision instruments[M].Beijing:Tsinghua University Press,2004(in Chinese))
[33]Zareian F,Medina R A.A practical method for proper modeling of structural damping in inelastic plane structural systems[J].Computers&Structures,2010,88(1):45-53
[34]Lin Y Y,Miranda E,Chang K C.Evaluation of damping reduction factors for estimating elastic response of structures with high damping[J].Earthquake Engineering&Structural Dynamics,2005,34(11):1427-1443
[35]Li Q S,Fang J Q,Jeary A P.Free vibration analysis of cantilevered tall structures under various axial loads[J].Engineering Structures,2000,22(5):525-534
[36]张辉东,王元丰,江辉.不同参数取值对复阻尼模型结构抗震性能的影响[J].建筑结构学报,2009,30(6):94-100(Zhang Huidong,Wang Yuanfeng,Jiang Hui.Effect of different parameters on seismic performance of complex damping structures[J].Journal of Building Structures,2009,30(6):94-100(in Chinese))
[37]Erduran E.Evaluation of Rayleigh damping and its influence on engineering demand parameter estimates[J].Earthquake Engineering&Structural Dynamics,2012,41(14):1905-1919
[38]Pant D R,Wijeyewickrema A C,El Gawady M A.Appropriate viscous damping for nonlinear time-history analysis of baseisolated reinforced concrete buildings[J].Earthquake Engineering&Structural Dynamics,2013,42(15):2321-2339