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Fractional order hybrid system dynamics
Author(s) -
Stevanović Hedrih Katica R.
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310008
Subject(s) - order (exchange) , eigenvalues and eigenvectors , mathematical analysis , mathematics , vibration , differential equation , discrete spectrum , fractional calculus , partial differential equation , dynamics (music) , physics , classical mechanics , quantum mechanics , finance , economics , acoustics
Dynamics of multi deformable bodies coupled by standard light fractional order discrete continuum layers is described by coupled partial fractional order differential equations. A mathematical analogy and phenomenological mapping between generalized coordinates of fractional order discrete chain systems and eigen time functions correspond to one of infinite numbers of eigen amplitude functions of dynamics of multi deformable bodies (beams, plates or membranes) coupled by standard light fractional order discrete continuum layers are identified. Eigen fractional order vibration modes are approximately determined analytically and graphically presented. A number of theorems is defined and proofed. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)