基于黏弹性理论的碰撞力计算方法及其在碰撞TMD中的应用
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摘要
针对地震作用下结构间的碰撞力的计算问题,结合黏弹性力学和接触力学理论,提出了一种基于黏弹性理论的碰撞力计算方法。推导该方法的计算公式,给出计算流程;根据已公开发表的钢-钢碰撞和混凝土-混凝土碰撞试验数据验证了该方法对于单次碰撞力计算的精确性。开展PTMD小型振动台试验,将该方法用于碰撞调谐质量阻尼器(PTMD)的碰撞力计算,验证该方法对于连续碰撞问题的有效性。结果表明:基于黏弹性理论的碰撞力计算方法对单次的弹性碰撞和非弹性碰撞均有较高精度;小型振动台试验结果与数值模拟符合较好,说明该方法也可以较精确地模拟钢材与黏弹性材料之间的连续多次碰撞问题; PTMD可以有效抑制结构在外激励作用下的位移响应,也可以加快结构在自由振动过程中的能量耗散,促使结构快速静止。
To calculate the pounding force between structures, an updated pounding force analysis method was put forward based on the viscoelastic mechanics and contact mechanics. The measuring formulas of the method were derived and the calculation process was proposed. Two existing pounding examples, steel to steel and concrete to concrete collisions, were re-calculated using the proposed method to verify its effectiveness for single impacts. A small scale shaking table test for pounding tuned mass damper(PTMD) was conducted and the proposed method was applied to calculate the pounding force for examining its effectiveness for continuous collisions. The results indicate that the proposed model can accurately simulate both elastic and plastic single collisions. The shaking table experimental results show a good agreement with the simulation results which demonstrate the accuracy of the proposed method for continuous collisions between steel and viscoelatic material. Moreover, the results confirm the control performance of the PTMD for suppressing displacement response of the structure under excitation, and the PTMD can improve the energy dissipation of structure and make the structure rapidly reaching stationary state in free vibration case.
To calculate the pounding force between structures, an updated pounding force analysis method was put forward based on the viscoelastic mechanics and contact mechanics. The measuring formulas of the method were derived and the calculation process was proposed. Two existing pounding examples, steel to steel and concrete to concrete collisions, were re-calculated using the proposed method to verify its effectiveness for single impacts. A small scale shaking table test for pounding tuned mass damper(PTMD) was conducted and the proposed method was applied to calculate the pounding force for examining its effectiveness for continuous collisions. The results indicate that the proposed model can accurately simulate both elastic and plastic single collisions. The shaking table experimental results show a good agreement with the simulation results which demonstrate the accuracy of the proposed method for continuous collisions between steel and viscoelatic material. Moreover, the results confirm the control performance of the PTMD for suppressing displacement response of the structure under excitation, and the PTMD can improve the energy dissipation of structure and make the structure rapidly reaching stationary state in free vibration case.
引文
[1]ANAGNOSTOPOULOS S A.Pounding of buildings in series during earthquakes[J].Earthquake Engineering&Structural Dynamics,1988,16(3):443-456.
[2]ANAGNOSTOPOULOS S A,SPILIOPOULOS K V.An investigation of earthquake induced pounding between adjacent buildings[J].Earthquake Engineering&Structural Dynamics,2010,21(4):289-302.
[3]CHOUW N,HAO H.Pounding damage to buildings and bridges in the 22 february 2011 christchurch earthquake[J].International Journal of Protective Structures,2012,3(2):123-140.
[4]薛启超,张井财,何建,等.地震作用下PTMD对高层钢结构的减振效果[J].哈尔滨工程大学学报,2017,38(3):412-418.XUE Qichao,ZHANG Jingcai,HE Jian,et al.Reducing vibration performance of pounding TMD on high-rise steel structures subject to seismic effects[J].Journal of Harbin Engineering University,2017,38(3):412-418.
[5]ZHANG P,SONG G,LI H N,et al.Seismic control of power transmission tower using pounding TMD[J].Journal of Engineering Mechanics,2013,139(10):1395-1406.
[6]LI H,ZHANG P,SONG G,et al.Robustness study of the pounding tuned mass damper for vibration control of subsea jumpers[J].Smart Material Structures,2015,24(9):095001.
[7]LI L,SONG G,SINGLA M,et al.Vibration control of a traffic signal pole using a pounding tuned mass damper with viscoelastic materials(II):experimental verification[J].Journal of Vibration&Control,2013,21(4):670-675.
[8]SONG G B,ZHANG P,LI L Y,et al.Vibration control of a pipeline structure using pounding tuned mass damper[J].Journal of Engineering Mechanics,2016,142(6):04016031.
[9]ZHANG P,LI L,PATIL D,et al.Parametric study of pounding tuned mass damper for subsea jumpers[J].Smart Materials&Structures,2016,25(1):15-28.
[10]XUE Q,ZHANG J,HE J,et al.Control performance and robustness of pounding tuned mass damper for vibration reduction in SDOF structure[J].Shock and Vibration,2016,2016(2):1-15.
[11]XUE Q,ZHANG J,HE J,et al.Seismic control performance for pounding tuned massed damper based on viscoelastic pounding force analytical method[J].Journal of Sound&Vibration,2017,411:362-377.
[12]GOLDSMITH W,FRASIER J T.Impact:the theory and physical behavior of colliding solids[J].Journal of Applied Mechanics,1961,28(4):639.
[13]ANAGNOSTOPOULOS S A.Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems[J].Earthquake Engineering&Structural Dynamics,2010,33(8):897-902.
[14]MUTHUKUMAR S,DESROCHES R.A hertz contact model with non-linear damping for pounding simulation[J].Earthquake Engineering&Structural Dynamics,2010,35(7):811-828.
[15]JANKOWSKI R.Non-linear viscoelastic modelling of earthquake-induced structural pounding[J].Earthquake Engineering&Structural Dynamics,2010,34(6):595-611.
[16]JANKOWSKI R.Analytical expression between the impact damping ratio and the coefficient of restitution in the nonlinear viscoelastic model of structural pounding[J].Earthquake Engineering&Structural Dynamics,2010,35(4):517-524.
[17]杨永强,李爽,谢礼立.构件跌落碰撞的数值模拟研究[J].振动与冲击,2010,29(6):54-58.YANG Yongqiang,LI Shuang,XIE Lili.Numerical simulation of component dropping collision[J].Journal of Vibration and Shock,2010,29(6):54-58.
[18]赵建伟,邹立华,方雷庆.考虑相邻建筑物碰撞的基础隔震结构的地震反应分析[J].振动与冲击,2010,29(5):215-219.ZHAO Jianwei,ZOU Lihua,FANG Leiqing.Seismic response analysis of base-isolated structures considering pounding of adjacent buildings[J].Journal of Vibration and Shock,2010,29(5):215-219.
[19]闫聚考,李建中,彭天波,等.大跨度悬索桥主引桥碰撞效应振动台试验及数值研究[J].振动与冲击,2017,36(7):234-240.YAN Jukao,LI Jianzhong,PENG Tianbo,et al.Shaking table tests and numerical analysis for pounding effect between main span and approach span of long-span suspension bridges[J].Journal of Vibration and Shock,2017,36(7):234-240.
[20]赵大海,刘勇,李宏男,等.隔震结构碰撞分析的改进Hertz-damp模型[J].振动与冲击,2017,36(12):236-242.ZHAO Dahai,LIU Yong,LI Hongnan,et al.Modified Hertzdamp model for base-isolated structural pounding[J].Journal of Vibration and Shock,2017,36(12):236-242.
[21]GOLAND M,WICKERSHAM P D,DENGLER M A.Propagation of elastic impact in beams in bending[J].Journal of Applied Mechanics 1955,22:1-7.
[22]约翰逊.接触力学[M].北京:高等教育出版社,1992.
[23]MIER J G M V,PRUIJSSERS A F,REINHARDT H W,et al.Load-time response of colliding concrete bodies[J].Journal of Structural Engineering,1991,117(2):354-374.
[2]ANAGNOSTOPOULOS S A,SPILIOPOULOS K V.An investigation of earthquake induced pounding between adjacent buildings[J].Earthquake Engineering&Structural Dynamics,2010,21(4):289-302.
[3]CHOUW N,HAO H.Pounding damage to buildings and bridges in the 22 february 2011 christchurch earthquake[J].International Journal of Protective Structures,2012,3(2):123-140.
[4]薛启超,张井财,何建,等.地震作用下PTMD对高层钢结构的减振效果[J].哈尔滨工程大学学报,2017,38(3):412-418.XUE Qichao,ZHANG Jingcai,HE Jian,et al.Reducing vibration performance of pounding TMD on high-rise steel structures subject to seismic effects[J].Journal of Harbin Engineering University,2017,38(3):412-418.
[5]ZHANG P,SONG G,LI H N,et al.Seismic control of power transmission tower using pounding TMD[J].Journal of Engineering Mechanics,2013,139(10):1395-1406.
[6]LI H,ZHANG P,SONG G,et al.Robustness study of the pounding tuned mass damper for vibration control of subsea jumpers[J].Smart Material Structures,2015,24(9):095001.
[7]LI L,SONG G,SINGLA M,et al.Vibration control of a traffic signal pole using a pounding tuned mass damper with viscoelastic materials(II):experimental verification[J].Journal of Vibration&Control,2013,21(4):670-675.
[8]SONG G B,ZHANG P,LI L Y,et al.Vibration control of a pipeline structure using pounding tuned mass damper[J].Journal of Engineering Mechanics,2016,142(6):04016031.
[9]ZHANG P,LI L,PATIL D,et al.Parametric study of pounding tuned mass damper for subsea jumpers[J].Smart Materials&Structures,2016,25(1):15-28.
[10]XUE Q,ZHANG J,HE J,et al.Control performance and robustness of pounding tuned mass damper for vibration reduction in SDOF structure[J].Shock and Vibration,2016,2016(2):1-15.
[11]XUE Q,ZHANG J,HE J,et al.Seismic control performance for pounding tuned massed damper based on viscoelastic pounding force analytical method[J].Journal of Sound&Vibration,2017,411:362-377.
[12]GOLDSMITH W,FRASIER J T.Impact:the theory and physical behavior of colliding solids[J].Journal of Applied Mechanics,1961,28(4):639.
[13]ANAGNOSTOPOULOS S A.Equivalent viscous damping for modeling inelastic impacts in earthquake pounding problems[J].Earthquake Engineering&Structural Dynamics,2010,33(8):897-902.
[14]MUTHUKUMAR S,DESROCHES R.A hertz contact model with non-linear damping for pounding simulation[J].Earthquake Engineering&Structural Dynamics,2010,35(7):811-828.
[15]JANKOWSKI R.Non-linear viscoelastic modelling of earthquake-induced structural pounding[J].Earthquake Engineering&Structural Dynamics,2010,34(6):595-611.
[16]JANKOWSKI R.Analytical expression between the impact damping ratio and the coefficient of restitution in the nonlinear viscoelastic model of structural pounding[J].Earthquake Engineering&Structural Dynamics,2010,35(4):517-524.
[17]杨永强,李爽,谢礼立.构件跌落碰撞的数值模拟研究[J].振动与冲击,2010,29(6):54-58.YANG Yongqiang,LI Shuang,XIE Lili.Numerical simulation of component dropping collision[J].Journal of Vibration and Shock,2010,29(6):54-58.
[18]赵建伟,邹立华,方雷庆.考虑相邻建筑物碰撞的基础隔震结构的地震反应分析[J].振动与冲击,2010,29(5):215-219.ZHAO Jianwei,ZOU Lihua,FANG Leiqing.Seismic response analysis of base-isolated structures considering pounding of adjacent buildings[J].Journal of Vibration and Shock,2010,29(5):215-219.
[19]闫聚考,李建中,彭天波,等.大跨度悬索桥主引桥碰撞效应振动台试验及数值研究[J].振动与冲击,2017,36(7):234-240.YAN Jukao,LI Jianzhong,PENG Tianbo,et al.Shaking table tests and numerical analysis for pounding effect between main span and approach span of long-span suspension bridges[J].Journal of Vibration and Shock,2017,36(7):234-240.
[20]赵大海,刘勇,李宏男,等.隔震结构碰撞分析的改进Hertz-damp模型[J].振动与冲击,2017,36(12):236-242.ZHAO Dahai,LIU Yong,LI Hongnan,et al.Modified Hertzdamp model for base-isolated structural pounding[J].Journal of Vibration and Shock,2017,36(12):236-242.
[21]GOLAND M,WICKERSHAM P D,DENGLER M A.Propagation of elastic impact in beams in bending[J].Journal of Applied Mechanics 1955,22:1-7.
[22]约翰逊.接触力学[M].北京:高等教育出版社,1992.
[23]MIER J G M V,PRUIJSSERS A F,REINHARDT H W,et al.Load-time response of colliding concrete bodies[J].Journal of Structural Engineering,1991,117(2):354-374.