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Dynamics of a Viscoelastic Rod of Fractional Derivative Type
Author(s) -
Atanackovic T.M.,
Stankovic B.
Publication year - 2002
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200206)82:6<377::aid-zamm377>3.0.co;2-m
Subject(s) - standard linear solid model , fractional calculus , viscoelasticity , uniqueness , type (biology) , mathematics , mathematical analysis , derivative (finance) , curvature , dynamics (music) , material derivative , time derivative , dissipation , physics , geometry , thermodynamics , acoustics , financial economics , economics , ecology , biology
We study dynamics of a viscoelastic rod with fractional derivative type of dissipation under time dependent loading. First the moment curvature relation for the rod from the generalized Zener model of a standard linear solid is derived. Then, we show that the dynamics of the problem is governed by a single linear differential equation with fractional derivative. The existence and uniqueness of solutions for this equation is studied in detail. The form of the solution for the case of periodic compressive force is also obtained.