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Fractional calculus applied to radiation damping
Author(s) -
Trinks C.,
Ruge P.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310118
Subject(s) - radiation damping , analogy , interpretation (philosophy) , fractional calculus , viscoelasticity , displacement (psychology) , stiffness , frequency domain , mathematics , mathematical analysis , calculus (dental) , physics , computer science , quantum mechanics , medicine , psychology , philosophy , linguistics , dentistry , psychotherapist , thermodynamics , programming language
Separate treatment of the low– and high–frequency part of the dynamic stiffness is essential when approximating the latter in the frequency–domain. In this paper, a doubly–asymptotic rational approximation of the low–frequency part is combined with an analytical interpretation of the asymptotic part leading to a system of fractional differential equations to represent the force–displacement relationship. Here, an analogy between fading memory of viscoelastic materials and radiation damping of unbounded domains is visible.