地震荷载作用下柔性支撑梁的动力响应分析
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摘要
提高结构在地震时的承载能力通常是从材料、截面形状等方面来考虑。在构件端部设置一定的约束支承也可以提高构件的抗震能力。为此,必须研究特定约束条件下梁在地震作用下的动力响应,这些约束表现为弹性支承刚度和阻尼特性。文中提出了一种等效单自由度分析方法,应用拉格朗日方程建立了端部弹性与阻尼支承梁的动力方程,并将动力计算结果与有限元计算结果对比验证单自由度分析方法的正确性。应用上述方法对地震作用下柔性支承梁的跨中相对位移、端部绝对位移以及弹性刚度、阻尼系数的敏感性进行了分析讨论。结果表明:等效单自由度分析方法计算准确,可以精确分析地震作用下柔性支撑梁的动力响应;合理设置弹性支承或弹性阻尼支承可以有效减小梁跨中与端部的相对位移,从而提高结构的抗震能力;但采用柔性支承减小构件相对位移的同时可能会增大构件端部的绝对位移。
Much attention has been paid to the properties of materials and the shapes of cross-sections of beams in order to increase the resistance of seismic loading structures.The seismic resistance of beams could be also increased effectively by setting some special constrained condition at the supports.The dynamic response of beams is investigated with flexible supports condition which show the elastic and damping feature.A simplified equivalent DOF analytical method of the beam with springs and dampers was established on basis of secondary Lagrange's dynamic equations.The dynamic response(relative displacement of the mid-span,the absolute displacement of the supports,the influences of the stiffness and damping coefficient and etc.) of beams is analyzed,the theoretical results are validated by ABAQUS numerical simulation method,Which shows that the equivalent DOF analytical method could precisely describe the dynamic response of beams with flexible supports subjected to seismic loading,and setting springs and dampers at the supports could reduced the displacement of the mid-span relative to the supports effectively,but it may increased the absolute displacements at the supports.
Much attention has been paid to the properties of materials and the shapes of cross-sections of beams in order to increase the resistance of seismic loading structures.The seismic resistance of beams could be also increased effectively by setting some special constrained condition at the supports.The dynamic response of beams is investigated with flexible supports condition which show the elastic and damping feature.A simplified equivalent DOF analytical method of the beam with springs and dampers was established on basis of secondary Lagrange's dynamic equations.The dynamic response(relative displacement of the mid-span,the absolute displacement of the supports,the influences of the stiffness and damping coefficient and etc.) of beams is analyzed,the theoretical results are validated by ABAQUS numerical simulation method,Which shows that the equivalent DOF analytical method could precisely describe the dynamic response of beams with flexible supports subjected to seismic loading,and setting springs and dampers at the supports could reduced the displacement of the mid-span relative to the supports effectively,but it may increased the absolute displacements at the supports.
引文
[1]方秦,杜茂林.爆炸荷载作用下弹性与阻尼支承梁的动力响应[J].力学与实践,2006,28(2):53-56.(FANG Qin,DU Maolin.Dynamic response of anelastically supported beams with damping subjected toblast loads[J].Mechanics in Engineering,2006,28(2):53-56.(in Chinese))
[2]Du MaoLin,Fang Qin,Chen Li.Analytical andNumerical Prediction for Dynamic Responses of anElastically and Damply Supported Beam Subjected toBlast Loads[C]//Proc.The 9th International Symposiumon Structural Engineering for Young Experts.Beijing:Science Press,2006.
[3]方秦,陈力,杜茂林.端部设置弹簧和阻尼器提高防护门抗力的理论与数值分析[J].工程力学,2008,25(3):194-199.(FANG Qin,CHEN Li,DU Maolin.Theoretical and numerical investigations into the effects ofsprings and dampers supported on ends on the increasingof the resistance of blast doors[J].EngineeringMechnics,2008,25(3):194-199.(in Chinese))
[4]宋春明,王明洋,唐正国.柔性动边界梁在横向撞击下的动力响应[J].解放军理工大学学报,2008,9(2):151-155.(SONG Chunming,WANG Mingyang,TANGZhengguo.Dynamic response of beams with flexiblesupports subject to transversal impact[J].Journal of PLAUniversity of Science and Technology,2008,9(2):151-155.(in Chinese))
[5]宋春明,王明洋,王德荣.爆炸荷载作用下柔性动边界拱的动力响应分析[J].兵工学报,2008,29(7):813-818.(SONG Chunming,WANG Mingyang,WANGDerong.Analysis of dynamic responses of arches withflexible supports subjected to blast loads[J].ActaArmamentar,2008,29(7):813-818.(in Chinese))
[2]Du MaoLin,Fang Qin,Chen Li.Analytical andNumerical Prediction for Dynamic Responses of anElastically and Damply Supported Beam Subjected toBlast Loads[C]//Proc.The 9th International Symposiumon Structural Engineering for Young Experts.Beijing:Science Press,2006.
[3]方秦,陈力,杜茂林.端部设置弹簧和阻尼器提高防护门抗力的理论与数值分析[J].工程力学,2008,25(3):194-199.(FANG Qin,CHEN Li,DU Maolin.Theoretical and numerical investigations into the effects ofsprings and dampers supported on ends on the increasingof the resistance of blast doors[J].EngineeringMechnics,2008,25(3):194-199.(in Chinese))
[4]宋春明,王明洋,唐正国.柔性动边界梁在横向撞击下的动力响应[J].解放军理工大学学报,2008,9(2):151-155.(SONG Chunming,WANG Mingyang,TANGZhengguo.Dynamic response of beams with flexiblesupports subject to transversal impact[J].Journal of PLAUniversity of Science and Technology,2008,9(2):151-155.(in Chinese))
[5]宋春明,王明洋,王德荣.爆炸荷载作用下柔性动边界拱的动力响应分析[J].兵工学报,2008,29(7):813-818.(SONG Chunming,WANG Mingyang,WANGDerong.Analysis of dynamic responses of arches withflexible supports subjected to blast loads[J].ActaArmamentar,2008,29(7):813-818.(in Chinese))
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