NDLI: Consistent Modelling of Infinite Beams by Fractional Dynamics

Content Provider	Springer Nature Link
Author	Ruge, Peter Trinks, Carolin
Copyright Year	2004
Abstract	For semi-infinite Euler–Bernoulli beams on elastic Winkler foundation, closed-form solutions can be derived analytically assuming a time-harmonic behaviour. For more general transient excitations and beam systems with local perturbations caused by nonlinear effects for example, an overall treatment of the system in the time-domain is desired. In this paper, the analytically obtained low-frequency dynamic stiffness of the semi-infinite beam in the frequency-domain is approximated by a rational function corresponding to a system of first-order differential equations in the time-domain. At the same time, the asymptotic part containing non-integer powers of the complex excitation frequency is interpreted as fractional derivatives of the unknown interface variables in a time-domain analysis. In addition to a summary of the above procedure, this paper contains the detailed description of two algorithms for the numerical solution of the resulting system of fractional differential equations to represent the force–displacement relationship of the semi-infinite beam.
Starting Page	267
Ending Page	284
Page Count	18
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	38
Issue Number	1-4
e-ISSN	1573269X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	dynamic stiffness fractional derivative infinite beam numerical solution of fractional differential equations rational approximation Mechanics Vibration, Dynamical Systems, Control Mechanical Engineering Automotive and Aerospace Engineering, Traffic
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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