Stability in parametric resonance of an axially moving beam constituted by fractional order material

DOI10.1007/S00419-012-0624-6zbMath1293.74232OpenAlexW2030947086MaRDI QIDQ396373

Bo Fang, Tian-Zhi Yang

Publication date: 13 August 2014

Published in: Archive of Applied Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00419-012-0624-6

zbMATH Keywords

instabilityparametric resonanceaxially moving beamfractional derivative Kelvin constitutive relationshipthe multi-scale method

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stability of dynamical problems in solid mechanics (74H55) Fractional derivatives and integrals (26A33) Linear constitutive equations for materials with memory (74D05)

Related Items (13)

Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations ⋮ Supercritical forced response of coupled motion of a nonlinear transporting beam ⋮ Stability analysis of a fractional viscoelastic plate strip in supersonic flow under axial loading ⋮ Nonlinear vibration analysis of fractional viscoelastic cylindrical shells ⋮ Stability analysis of viscoelastic pipes conveying fluid with different boundary conditions described by fractional Zener model ⋮ Primary and secondary resonances in pipes conveying fluid with the fractional viscoelastic model ⋮ Stability and bifurcation analysis of single-degree-of-freedom linear vibro-impact system with fractional-order derivative ⋮ Stochastic P-bifurcation of a bistable viscoelastic beam with fractional constitutive relation under Gaussian white noise ⋮ Dynamic stability of an axially transporting beam with two-frequency parametric excitation and internal resonance ⋮ Analytical analysis on nonlinear parametric vibration of an axially moving string with fractional viscoelastic damping ⋮ Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid ⋮ Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions ⋮ Primary and secondary resonance responses of fractional viscoelastic PET membranes

Cites Work

• Equilibria of axially moving beams in the supercritical regime
• Nonlinear dynamic response of axially moving, stretched viscoelastic strings
• Asymptotic nonlinear behaviors in transverse vibration of an axially accelerating viscoelastic string
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Two-dimensional rheological element in modelling of axially moving viscoelastic web
• Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law
• Classical Vibration Analysis of Axially Moving Continua
• SUPERCRITICAL SPEED STABILITY OF THE TRIVIAL EQUILIBRIUM OF AN AXIALLY-MOVING STRING ON AN ELASTIC FOUNDATION

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