Interconversion of Prony series for relaxation and creep
Interconversion of Prony series for relaxation and creep
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DOI：
10.1122/1.4929398
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发表时间：
2015-09-01
影响因子：
3.3
通讯作者：
Anderssen, R. S.
中科院分区：
文献类型：
--
作者：
Loy, R. J.;de Hoog, F. R.;Anderssen, R. S.
当用Prony级数表示松弛模量和蠕变模量G（t）和J（t）时，已经提出了各种算法来求解线性粘弹性的相互转换方程。对于G（t）的Prony级数，恢复J（t）的Prony级数的关键步骤是确定J（t）中各项的系数{j（k）}。这里，通过根据G（t）的cap（s）上的拉普拉斯变换（G）的cap（s）上的导数d（G）/ds导出{j（k）}的初等且容易评估的解析公式，避免了求解{j（k）}的不良条件矩阵方程的需要。(C)2015年，美国流变学会（Society of Rheology）
Various algorithms have been proposed to solve the interconversion equation of linear viscoelasticity when Prony series are used for the relaxation and creep moduli, G(t) and J(t). With respect to a Prony series for G(t), the key step in recovering the corresponding Prony series for J(t) is the determination of the coefficients {j(k)} of terms in J(t). Here, the need to solve a poorly conditioned matrix equation for the {j(k)} is circumvented by deriving elementary and easily evaluated analytic formulae for the {j(k)} in terms of the derivative d (G) over cap (s)/ds of the Laplace transform (G) over cap (s) of G(t). (C) 2015 The Society of Rheology.