黏弹性松弛函数的积分表示（英文）
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摘要
讨论了松弛函数的积分表示.用Laplace变换方法得到了Maxwell模型的应力应变关系方程,方程中的松弛函数可以用Mittag-Leffler函数表示.由于大的负变元的存在,计算起来非常困难,运用连续松驰谱法将Mittag-Leffler函数用积分的形式来表示,从而解决了这个问题.通过数值算例说明了该结果的有效性.
In this paper,the integral representation of relaxation function is discussed.The stress-strain relationship equation of Maxwell model is obtained by Laplace transformation.The relaxation function in the equation can be expressed by Mittag-Leffler function.Because of the existence of large negative arguments,it is very difficult to calculate.We use the continuous relaxation spectrum to express the Mittag-Leffler function in integral form.This problem has been solved.A numerical example illustrates the effectiveness of the result.
In this paper,the integral representation of relaxation function is discussed.The stress-strain relationship equation of Maxwell model is obtained by Laplace transformation.The relaxation function in the equation can be expressed by Mittag-Leffler function.Because of the existence of large negative arguments,it is very difficult to calculate.We use the continuous relaxation spectrum to express the Mittag-Leffler function in integral form.This problem has been solved.A numerical example illustrates the effectiveness of the result.
引文
[1]PODLUBNY I.Fractional Differential Equation[M].San Diego:Academic Press,1999.
[2]LONG J M,XIAO R,CHEN W.Fractional viscoelastic models with non-singular kernels[J].Mechanics of Materials2018,127:55-64.
[3]WU C X,YUAN J,SHI B.Stability of initialization response of fractional oscillators[J].Journal of Vibroengineering2016,18(6):6-9.
[4]OLDHAM K S,SPANIER J.The Fractional Calculus[M].New York:Academic Press,1974.
[5]YUAN J.Sliding mode control of vibration in single-degree-of-freedom fractional oscillators[J].Journal of Dynamic Systems,Measurement and Control,2016,139(5):1 14503-114506.
[6]ADHIKARI S.Dynamic response characteristics of a nonviscously damped oscillator[J].Journal of Applied Mechanics,2008,75(1):148-155.
[7]HAUPT P,LION A,BACKHAUS E.On the dynamic behaviour of polymers under finites:constitutive modelling and identification of parameters[J].Solids Struct,2000,37(26):3633-3646.
[8]HAUPT P,LION A.On finite linear viscoelasticity of incompressible isotropic materials[J].Acta Mechanica,2002,159(1/2/3/4):87-124.
[9]DIETHELM K.The Analysis of Fractional Differential Equations[M].Heidelberg:Springer,2010.
[10]TSCHOEGL N W.The Phenomenological Theory of Linear Viscoelastic Material Behaviour[M].Berlin:Springer,1989.
[2]LONG J M,XIAO R,CHEN W.Fractional viscoelastic models with non-singular kernels[J].Mechanics of Materials2018,127:55-64.
[3]WU C X,YUAN J,SHI B.Stability of initialization response of fractional oscillators[J].Journal of Vibroengineering2016,18(6):6-9.
[4]OLDHAM K S,SPANIER J.The Fractional Calculus[M].New York:Academic Press,1974.
[5]YUAN J.Sliding mode control of vibration in single-degree-of-freedom fractional oscillators[J].Journal of Dynamic Systems,Measurement and Control,2016,139(5):1 14503-114506.
[6]ADHIKARI S.Dynamic response characteristics of a nonviscously damped oscillator[J].Journal of Applied Mechanics,2008,75(1):148-155.
[7]HAUPT P,LION A,BACKHAUS E.On the dynamic behaviour of polymers under finites:constitutive modelling and identification of parameters[J].Solids Struct,2000,37(26):3633-3646.
[8]HAUPT P,LION A.On finite linear viscoelasticity of incompressible isotropic materials[J].Acta Mechanica,2002,159(1/2/3/4):87-124.
[9]DIETHELM K.The Analysis of Fractional Differential Equations[M].Heidelberg:Springer,2010.
[10]TSCHOEGL N W.The Phenomenological Theory of Linear Viscoelastic Material Behaviour[M].Berlin:Springer,1989.