分数导数粘滞阻尼器减震结构的随机地震响应与等效阻尼
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摘要
对分数导数粘滞阻尼器单自由度耗能结构的随机地震响应与等效阻尼进行了系统研究。建立了结构运动方程;应用随机平均法,将结构响应幅值近似为扩散过程,获得了结构位移与速度联合概率密度函数和位移、速度响应方差的解析解;基于与随机平均分析完全相同的等效准则,建立了可直接应用反应谱法的上述阻尼器的等效阻尼计算公式,算例分析表明了所得公式的合理性。
Random earthquake response and equivalent damping of SDOF dissipation structure with fractional derivative viscous dampers are studied systematically.The dynamic equations of structure are firstly established.By the stochastic averaging method,structural amplitude is approximated to diffusion process,the exact solutions of joint probability density and mean-square values of structural displacement and velocity are completed.From equivalent criterion of stochastic averaging analysis,the analytics formulas of equivalent damping of fractional derivative viscous dampers are established.Thus it is possible for structure to use response spectrum.An example is shown in these methods,and the proposed formula is analyzed.
Random earthquake response and equivalent damping of SDOF dissipation structure with fractional derivative viscous dampers are studied systematically.The dynamic equations of structure are firstly established.By the stochastic averaging method,structural amplitude is approximated to diffusion process,the exact solutions of joint probability density and mean-square values of structural displacement and velocity are completed.From equivalent criterion of stochastic averaging analysis,the analytics formulas of equivalent damping of fractional derivative viscous dampers are established.Thus it is possible for structure to use response spectrum.An example is shown in these methods,and the proposed formula is analyzed.
引文
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[8]刘林超,闫启方.分数导数Kelvin黏弹性梁的弯曲分析[J].信阳师范学院学报:自然科学版,2010,23(3):378-382.
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[14]Wahi P,Chatterjee A.Averaging oscillations with smallfractional damping and delayed terms[J].Nonlinear Dy-namics,2004,38(1-4):3-22.
[15]Huang Z L,Jin X L.Response and stability of a SDOFstrongly nonlinear stochastic system with light damping mod-eled by a fractional derivative[J].Journal of Sound andVibration,2009,319(3-5):1121-1135.
[16]Tseng C C,Pei S C,Hsia S C.Computation of fractionalderivative using Fourier transform and digital FIR differentia-tor[J].Signal Processing,2000,80(1):151-159.
[17]李创第,李暾.结构在水平与竖向随机地震同时作用下的相关函数和谱密度[J].工程力学,2008,25(8):156-163.
[18]李创第,邹万杰,黄天立,等.结构在水平与竖向地震同时作用的非平稳响应[J].土木工程学报,2005,38(6):25-34.
[19]黄冬梅,李创第,陈俊忠,等.结构—土相互作用体系的地震作用取值——基于规范地震动模型的复模态时域法[J].振动工程学报,2006,19(4):571-577.
[20]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[21]黄冬梅,李创第,朱乐东.基础隔震结构基于设计反应谱的地震作用取值[J].西安建筑科技大学学报,2007,39(4):504-511.
[22]李创第,陈俊忠,黄冬梅.单自由度“加层”减震结构地震作用取值的复模态法[J].应用力学学报,2007,24(1):160-164.
[23]李创第,陈俊忠,黄冬梅,等.多自由度“加层”减震结构地震作用取值的复模态法[J].哈尔滨工业大学学报,2009,41(4):201-203.
[24]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.
[2]周锡元,阎维明,杨润林.建筑结构的隔震、减振和振动控制[J].建筑结构学报,2002,23(2):2-12.
[3]周云.耗能减震加固技术与设计方法[M].北京:科学出版社,2006.
[4]李创第,葛新广,朱倍权.带五种被动减振器的高层建筑基于Davenport谱随机风振响应的解析解法[J].工程力学,2009,33(4):151-152.
[5]李创第,黄天立,李暾,等.TMD控制优化设计与振动台试验研究[J].土木工程学报,2006,39(7):19-25.
[6]李创第,夏立志,葛新广,等.Maxwell粘滞阻尼器耗能结构的随机地震响应[J].桂林理工大学学报,2011,31(1):61-67.
[7]孙海忠,张卫.服从分数导数Kelvin本构模型的粘弹性阻尼器的阻尼性能分析及试验研究[J].振动工程学报,2008,21(1):48-53.
[8]刘林超,闫启方.分数导数Kelvin黏弹性梁的弯曲分析[J].信阳师范学院学报:自然科学版,2010,23(3):378-382.
[9]周云.粘弹性阻尼减震结构设计[M].武汉:武汉理工大学出版社,2006.
[10]Makris N,Constantinou M,Dargush G F.Analytical modelof viscoelastic fluid dampers[J].Journal of Structural Engi-neering,1993,119(11):3310-3325.
[11]Makris N,Constantinou MC.Fractional derivative Maxwellmodel for viscous dampers[J].Journal of Structural Engeer-ing,1991,117(9):2708-2724.
[12]Zhu W Q,Cai G Q.Nonlinear stochastic dynamics:a sur-vey of recent developments[J].Acta Mechanica Sinica,2002,18(6):551-566.
[13]朱位秋.随机振动[M].北京:科学出版社,1998.
[14]Wahi P,Chatterjee A.Averaging oscillations with smallfractional damping and delayed terms[J].Nonlinear Dy-namics,2004,38(1-4):3-22.
[15]Huang Z L,Jin X L.Response and stability of a SDOFstrongly nonlinear stochastic system with light damping mod-eled by a fractional derivative[J].Journal of Sound andVibration,2009,319(3-5):1121-1135.
[16]Tseng C C,Pei S C,Hsia S C.Computation of fractionalderivative using Fourier transform and digital FIR differentia-tor[J].Signal Processing,2000,80(1):151-159.
[17]李创第,李暾.结构在水平与竖向随机地震同时作用下的相关函数和谱密度[J].工程力学,2008,25(8):156-163.
[18]李创第,邹万杰,黄天立,等.结构在水平与竖向地震同时作用的非平稳响应[J].土木工程学报,2005,38(6):25-34.
[19]黄冬梅,李创第,陈俊忠,等.结构—土相互作用体系的地震作用取值——基于规范地震动模型的复模态时域法[J].振动工程学报,2006,19(4):571-577.
[20]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998.
[21]黄冬梅,李创第,朱乐东.基础隔震结构基于设计反应谱的地震作用取值[J].西安建筑科技大学学报,2007,39(4):504-511.
[22]李创第,陈俊忠,黄冬梅.单自由度“加层”减震结构地震作用取值的复模态法[J].应用力学学报,2007,24(1):160-164.
[23]李创第,陈俊忠,黄冬梅,等.多自由度“加层”减震结构地震作用取值的复模态法[J].哈尔滨工业大学学报,2009,41(4):201-203.
[24]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.
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