Representation of radiation damping by fractional time derivatives | Zendy

Ruge P. | Zendy; Trinks C. | Zendy

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Representation of radiation damping by fractional time derivatives

Author(s) -

Ruge P.,

Trinks C.

Publication year - 2003

Publication title -

earthquake engineering and structural dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.218

H-Index - 127

eISSN - 1096-9845

pISSN - 0098-8847

DOI - 10.1002/eqe.264

Subject(s) - displacement (psychology) , radiation damping , fractional calculus , representation (politics) , mathematics , stiffness matrix , mathematical analysis , stiffness , interpretation (philosophy) , matrix (chemical analysis) , derivative (finance) , domain (mathematical analysis) , differential (mechanical device) , frequency domain , time domain , physics , computer science , politics , political science , law , psychology , materials science , particle physics , financial economics , computer vision , economics , composite material , psychotherapist , thermodynamics , programming language

When modelling unbounded domains, formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance. In this paper, a method to describe the dynamic stiffness by a system of fractional differential equations in the time‐domain is presented. Here, a doubly asymptotic rational approximation of the low‐frequency force–displacement relationship is used, whereas a direct interpretation of the asymptotic part as a fractional derivative is possible. The numerical solution of the corresponding system of fractional differential equations is demonstrated using the infinite beam on elastic foundation as an example. Copyright © 2003 John Wiley & Sons, Ltd.

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