ISSN:
1435-1528
Keywords:
Linear viscoelasticity
;
complex modulus
;
complex compliance
;
relaxation and retardation spectrum
;
approximative determination
;
delta-function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
Abstract A function series g(x; n, m) is presented that converges in the limiting case n→∞ and m = constant to the delta-function located at x = ωλ = 1. For every finite n, there exists 2n+1(−n≤m≤n) approximations of the delta-function δ(n)(x−x n,m ). x n,m is the argument where the function reaches its maximum. A formula for the calculation is given. The delta-function approximation is the starting point for the approximative determination of the logarithmic density function of the relaxation or retardation time spectrum. The n-th approximation of density functions based on components of the complex modulus (G*) or the complex compliance (J*) is given. It represents an easy differential operator of order n. This approach generalizes the results obtained by Schwarzl and Staverman, and Tschoegl. The symmetry properties of the approximations are explained by the symmetry properties of the function g(x; n, m). Therefore, the separate equations for each approximation given by Tschoegl can be subsumed in a single equation for G′ and G″, and in another for J′ and J″.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00366789
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