分数阶Kelvin模型描述的单质点基础隔振体系动力特性分析
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摘要
利用分数导数的性质和粘弹性理论得到分数阶Kelvin模型描述的单自由度基础隔震体系的隔震结构加速度响应衰减比和位移响应放大比,并研究分数导数的阶数、阻尼比和频率比对隔震结构位移响应放大比的影响,研究表明:分数导数的阶数和阻尼比对隔震结构位移响应放大比的影响较大,阻尼比对分数导数Kelvin模型和经典粘弹性模型描述的隔震结构位移响应放大比的影响规律存在不同,且分数导数模型的应用范围较广。
Regarding the isolation layers as viscoelastic materials,the decay ratio of acceleration response and amplification ratio of displacement response of isolation structure for single-particle vibration-isolation system described by fractional Kelvin model are obtained.The influences of the order of fractional derivative,damping ratio and frequency ratio on the amplification ratio of displacement response of the isolation structure are investigated.The result shows that the order of fractional derivative and damping ratio have a great influence on the amplification ratio of displacement response of the isolation structure.However,the influences of damping ratio on the amplification ratio of displacement response of the isolation structure described by,respectively,fractional Kelvin model and classical model are different.And the fractional-order derivative model is more extensively applicable.
Regarding the isolation layers as viscoelastic materials,the decay ratio of acceleration response and amplification ratio of displacement response of isolation structure for single-particle vibration-isolation system described by fractional Kelvin model are obtained.The influences of the order of fractional derivative,damping ratio and frequency ratio on the amplification ratio of displacement response of the isolation structure are investigated.The result shows that the order of fractional derivative and damping ratio have a great influence on the amplification ratio of displacement response of the isolation structure.However,the influences of damping ratio on the amplification ratio of displacement response of the isolation structure described by,respectively,fractional Kelvin model and classical model are different.And the fractional-order derivative model is more extensively applicable.
引文
[1]胡智渊.粘弹性阻尼器隔震结构的振动控制研究[J].华东交通大学学报,2008,25(3):32-35.
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[3]刘再华,丁强.地基-基础隔震结构系统的动力响应[J].武汉城市建设学院学报,1995,12(2):44-51.
[4]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[5]SHIMIZU Nobuyuki,ZHANG Wei.Fractional calculusapproach to dynamic problem of viscoelastic materials[J].JSMEInternational Journal,Series C,1999,1(42):827-830.
[6]I.Podlubny.Fractional differential equation.An introduc-tion to fractional derivatives,fractional differential equa-tions,some methods of their solution and some of theirapplications[M].Academic Press,San Diego-Boston-NewYork-London-Tokyo-Toronto,1999.
[2]林皋,栾茂田,陈怀海.土-结构相互作用对高层建筑非线性地震响应的影响[J].木工程学报,1993,26(4):1-13.
[3]刘再华,丁强.地基-基础隔震结构系统的动力响应[J].武汉城市建设学院学报,1995,12(2):44-51.
[4]刘林超,张卫.具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性[J].岩土力学,2005,26(2):287-289.
[5]SHIMIZU Nobuyuki,ZHANG Wei.Fractional calculusapproach to dynamic problem of viscoelastic materials[J].JSMEInternational Journal,Series C,1999,1(42):827-830.
[6]I.Podlubny.Fractional differential equation.An introduc-tion to fractional derivatives,fractional differential equa-tions,some methods of their solution and some of theirapplications[M].Academic Press,San Diego-Boston-NewYork-London-Tokyo-Toronto,1999.
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