Application of fractional calculus in the dynamics of beams

DOI10.1186/1687-2770-2012-135zbMath1278.35014OpenAlexW1973269734WikidataQ59272088 ScholiaQ59272088MaRDI QIDQ384534

D. Dönmez Demir, Necdet Bıldık, Berra Gültekin Sinir

Publication date: 28 November 2013

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2012-135

zbMATH Keywords

method of multiple scalesstability boundariesperturbation methodfractional derivativeparametric resonanceslinear vibrationsviscoelastic beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stability in context of PDEs (35B35) Linear constitutive equations for materials with memory (74D05) Fractional partial differential equations (35R11)

Related Items (6)

Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness ⋮ Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay ⋮ A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay ⋮ Linear dynamical analysis of fractionally damped beams and rods ⋮ Fractional differential equations and Volterra-Stieltjes integral equations of the second kind ⋮ Infinite mode analysis of a general model with external harmonic excitation

Cites Work

• A finite difference method for fractional partial differential equation
• Non-linear vibrations and stability of an axially moving beam with time-dependent velocity
• Formulation of Euler-Lagrange equations for fractional variational problems
• Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law
• A COMPARISON OF DIFFERENT VERSIONS OF THE METHOD OF MULTIPLE SCALES FOR PARTIAL DIFFERENTIAL EQUATIONS
• Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed
• Comparison of direct-perturbation methods with discretization-perturbation methods for non-linear vibrations

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