分数导数型粘弹性阻尼器的动力学有限元方程及数值解
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摘要
采用分数导数Kelvin固体模型建立粘弹性阻尼器在外力作用下的分数阶动力学有限元方程,并利用New-mark数值积分法得到数值解。结果表明,Zhang and Shimizu分数导数数值积分法能够很好地满足精度、收敛性和稳定性等要求,通过减小时间步长能够有效减小因引入Newmark而导致的周期误差,从而提高计算精度。
A dynamic FE equation of the viscoelastic damper under applied stress was built based on fractional derivative Kelvin solid model,and the numerical solution was obtained by Newmark numerical integration method.The results showed that ZHANG and Shimizu's fractional derivative numerical integration method met the requirements for accuracy,convergence and constance,and decreased the periodic error from the introduction of Newmark by reducing the time interval resulting in more accuracy of calculation.
A dynamic FE equation of the viscoelastic damper under applied stress was built based on fractional derivative Kelvin solid model,and the numerical solution was obtained by Newmark numerical integration method.The results showed that ZHANG and Shimizu's fractional derivative numerical integration method met the requirements for accuracy,convergence and constance,and decreased the periodic error from the introduction of Newmark by reducing the time interval resulting in more accuracy of calculation.
引文
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[4]白立来,胡传忻,王国红,等.粘弹性阻尼器的研究[J].北京工业大学学报,1998,24(4):69-72.
[5]刘季,陈月明.粘弹性阻尼器结构的减震研究[J].哈尔滨建筑大学学报,1998,31(15):1-6.
[6]徐赵东,周洲,赵鸿铁,等.粘弹性阻尼器的计算模型[J].工程力学,2001,18(6):88-92.
[7]Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[8]Zhang W,Shi mizu N.Numerical algorithmfor dynamic pro-blems involving fractional operators[J].JSME InternationalJournal(Series C),1998,41(3):364-370.
[9]Oldham K B,Spanier J.The Fractional Calculus[M].NewYork:Academic,1974.
[10]Zhang W,Shi mizu N,Xu H.Thermal effects of the visco-elastic materials described byfractional calculus constitutivelaw[A].The First Asian Conference on Multibody Dy-namics 2002.Iwaki,Japan:2002-07-31~08-02.
[11]Koller R C.Polynomial operators Stielties convolution andfractional calculus in hereditary mechanics[J].Acta Me-chanics,1986,58:251-254.
[12]王勋成.有限单元法[M].北京:清华大学出版社,2003.
[2]吴波,郭安薪.设有粘弹性阻尼器的结构体系的受力分析[J].地震工程与工程振动,1998,14(3):6-14.
[3]柴键.粘弹性阻尼器的动态特性研究[J].甘肃工业大学学报,1995,21(1):42-45.
[4]白立来,胡传忻,王国红,等.粘弹性阻尼器的研究[J].北京工业大学学报,1998,24(4):69-72.
[5]刘季,陈月明.粘弹性阻尼器结构的减震研究[J].哈尔滨建筑大学学报,1998,31(15):1-6.
[6]徐赵东,周洲,赵鸿铁,等.粘弹性阻尼器的计算模型[J].工程力学,2001,18(6):88-92.
[7]Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[8]Zhang W,Shi mizu N.Numerical algorithmfor dynamic pro-blems involving fractional operators[J].JSME InternationalJournal(Series C),1998,41(3):364-370.
[9]Oldham K B,Spanier J.The Fractional Calculus[M].NewYork:Academic,1974.
[10]Zhang W,Shi mizu N,Xu H.Thermal effects of the visco-elastic materials described byfractional calculus constitutivelaw[A].The First Asian Conference on Multibody Dy-namics 2002.Iwaki,Japan:2002-07-31~08-02.
[11]Koller R C.Polynomial operators Stielties convolution andfractional calculus in hereditary mechanics[J].Acta Me-chanics,1986,58:251-254.
[12]王勋成.有限单元法[M].北京:清华大学出版社,2003.
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