简化波动方法分析结构竖向脉冲效应的反射与透射系数
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摘要
近场竖向地震波富含各频率成分且具用较大的传播速度可能对结构造成较强的竖向脉冲效应。应用波动力学来分析脉冲型纵波激励作用下多自由度体系的动态响应时,其计算过程过于复杂且不容易收敛,而振动力学又无法反映波传播的时滞性和反射叠加效应,不能很好地反映这种脉冲效应和描述该类激励对结构造成的应力损伤。该文结合振动力学和波动力学的各自特点,针对简化的结构层模型并考虑了阻尼效应,推导了纵波通过楼板集中质量的反射和透射系数。在此基础上,对阻尼比、轴向刚度比和质量比对反射系数和透射系数的影响进行了参数分析,并对这些系数在土体-结构相互作用中的应用进行了初步的研究。研究结果表明:在反射和透射系数中考虑阻尼的影响是十分必要的,反射和透射系数的幅频曲线体现出了显著的高频滤波效应,且受轴向刚度比和质量比的影响也较大。这些研究工作为之后应用此简化波动方法计算脉冲型地震动竖向分量作用下结构的动力响应奠定了基础。
Some structures may be subjected to a strong impulse effect under a near-fault vertical seismic wave with various frequency components and large propagation speed.When the wave propagation method is used to analyze the dynamic responses of multi-degree-of-freedom(MDOF) systems under impulse-type longitudinal excitations,the computational process is generally sophisticated and not easy to converge.It is also not desirable to apply vibration mechanics to reflect the impulse effect and depict stress wave-induced damage since it cannot well reflect the time delay and reflection of stress waves propagate through floors.The wave propagation method has been combined with vibration mechanics herein to derive the reflection and transmission coefficients of longitudinal wave propagates through simplified lumped masses at floors in which the damping effect is considered.Based on this,a parametric study was carried out to investigate the effects of the damping ratio,axial stiffness ratio and mass ratio on these coefficients.A further discussion on the possible application of the coefficients to studying the interaction between soil and superstructures was performed as well.The results from this paper indicate that it is very necessary to consider the damping ratio in the reflection and transmission coefficients.The relationship curves between amplitude and frequency curves have shown a significant high-frequency filter effect and a strong dependence on axial stiffness and mass ratio.The investigation could form the basis of using the simplified wave propagation method to evaluate the dynamic responses of MDOFs excited by the impulse-type vertical component of near-fault strong ground motions.
Some structures may be subjected to a strong impulse effect under a near-fault vertical seismic wave with various frequency components and large propagation speed.When the wave propagation method is used to analyze the dynamic responses of multi-degree-of-freedom(MDOF) systems under impulse-type longitudinal excitations,the computational process is generally sophisticated and not easy to converge.It is also not desirable to apply vibration mechanics to reflect the impulse effect and depict stress wave-induced damage since it cannot well reflect the time delay and reflection of stress waves propagate through floors.The wave propagation method has been combined with vibration mechanics herein to derive the reflection and transmission coefficients of longitudinal wave propagates through simplified lumped masses at floors in which the damping effect is considered.Based on this,a parametric study was carried out to investigate the effects of the damping ratio,axial stiffness ratio and mass ratio on these coefficients.A further discussion on the possible application of the coefficients to studying the interaction between soil and superstructures was performed as well.The results from this paper indicate that it is very necessary to consider the damping ratio in the reflection and transmission coefficients.The relationship curves between amplitude and frequency curves have shown a significant high-frequency filter effect and a strong dependence on axial stiffness and mass ratio.The investigation could form the basis of using the simplified wave propagation method to evaluate the dynamic responses of MDOFs excited by the impulse-type vertical component of near-fault strong ground motions.
引文
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[2]周靖,周飞,蔡健,王里佳.脉冲型竖向地震作用下大跨度RC带腋撑框架结构弹塑性动力响应分析[J].工程力学,2010,27(6):113―119.Zhou Jing,Zhou Fei,Cai Jian,Wang Lijia.Seismicelastic-plastic response of long-span RC frame structurewith haunched members subjected to pulse-like verticalground motions[J].Engineering Mechanics,2010,27(6):113―119.(in Chinese)
[3]Desmond T P.Theoretical and experimental investigationof stress waves at a junction of three bars[J].Journal ofApplied Mechanics,1999,48(1):148―154.
[4]黄中伟,杨磊.应力冲击波在结构节点的反射和透射[J].深圳大学学报理工版,2007,24(1):9―12.Huang Zhongwei,Yang Lei.Reflection and transmissionof stress shock wave at structure node[J].Journal ofShenzhen University Science and Engineering,2007,24(1):9―12.(in Chinese)
[5]李东升,贾辉,李宏男,等.论高耸结构地震动响应的时延性[J].建筑结构,2010,40(增刊):119―113.Li Dongsheng,Jia Hui,Li Hongnan,et al.Time delay ofearthquake excitation in high-rise building[J].BuildingStructures,2010,40(supplment):119―113.(in Chinese)
[6]Chen J Y,Chen H L,Pan E.Reflection and transmissioncoefficients of plane waves in magnetoelectroelasticlayered structures[J].Journal of Vibration and Acoustics,2008,130(3):1―7.
[7]王礼立.应力波基础[M].第2版.北京:国防工业出版社,2005.Wang Lili.Foundation of Stress Waves[M].2nd ed.Beijing:National Defence Industry Press,2005.(inChinese)
[8]Zhang R R,Snieder R,Gargab L,et al.Modeling ofseismic wave motion in high-rise buildings[J].Probabilistic Engineering Mechanics,2011,26(4):520―527.
[9]Safak E.Propagation of seismic waves in tall buildings[J].The Structural Design of Tall Building,1998,7(4):295―306.
[10]刘见华,金咸定.梁结构耦合点的纵向弹性波传播[J].振动与冲击,2004,23(4):54―57.Liu Jianhua,Jin Xianding.Longitudinal elastic wavetransmission through a coupling joint in beam structures[J].Journal of Vibration and Shock,2004,23(4):54―57.(in Chinese).
[11]吴斌,韩强,杨桂通.平面杆系结构弹性波传播的实验研究[J].实验力学,1998,13(4):502―508.Wu Bin,Han Qiang,Yang Guitong.An experimentalstudy on the elastic waves in plane framed rods[J].Journal of Experimental Mechanics,1998,13(4):502―508.(in Chinese)
[12]Samiee A,Isaacs J,Nemat-Nasser S.A numerical andexperimental study of high strain-rate compression andtension response of concrete[C]//Proceeding of theSEM Annual Conference Indianapolis,Indiana USA,2010.
[13]王阜,廖振鹏.烟囱竖向地震反应的波动分析[J].土木工程学报,1984,37(1):12―26.Wang Fu,Liao Zhenpeng.Wave motion response ofchimneys to vertical ground motion[J].China CivilEngineering Journal,1984,37(1):12―26.(in Chinese)
[14]Kohler M D,Heaton T H,Bradford S C.Propagatingwaves in the steel,moment-frame factor buildingrecorded during earthquakes[J].Bulletin ofSeismological Society of America,2007,97(4):1334―1345.
[15]Lu X,Lu X Z,Zhang W K,et al.Collapse simulation ofa super high-rise building subjected to extremely strongearthquakes[J].Science China Technological Sciences,2011,54(10):2549―2560.
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