Analytical analysis on nonlinear parametric vibration of an axially moving string with fractional viscoelastic damping
type: Item
instance of: scholarly article
title: Analytical analysis on nonlinear parametric vibration of an axially moving string with fractional viscoelastic damping
zbMATH Open document ID: 1426.74177
DOI: 10.1155/2017/1393954
author: Ying Li
author: Ye Tang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton's second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff's fractional material model are much larger than those predicted by Mote's fractional material model.
Mathematics Subject Classification ID: 74K05
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 6971734
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1393954
OpenAlex ID: W2769197569
cites work: Classical Vibration Analysis of Axially Moving Continua
cites work: Transverse Vibration of an Axially Accelerating String
cites work: Non-linear vibrations and stability analysis of tensioned pipes conveying fluid with variable velocity
cites work: Reliability and sensitivity analysis of an axially moving beam
cites work: Linear and nonlinear modal analysis of the axially moving continua based on the invariant manifold method
cites work: Vertical dynamic response of pile embedded in layered transversely isotropic soil
cites work: Dynamic stability of an axially accelerating viscoelastic beam
cites work: Stability characteristics of an axially accelerating string supported by an elastic foundation
cites work: Two-frequency parametric excitation and internal resonance of a moving viscoelastic beam
cites work: Non-linear free oscillations of moving viscoelastic belts
cites work: Parametric and internal resonances of in-plane accelerating viscoelastic plates
cites work: Zener internal damping in modelling of axially moving viscoelastic beam with time-dependent tension
cites work: Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle
cites work: Stability of axially accelerating viscoelastic beams: Multi-scale analysis with numerical confirmations
cites work: Transient responses of an axially accelerating viscoelastic string constituted by a fractional differentiation law
cites work: Non-linear vibration of a traveling tensioned beam
cites work: Asymptotic analysis of axially accelerating viscoelastic strings
cites work: Q3864730
cites work: Stability in parametric resonance of an axially moving beam constituted by fractional order material
description: scientific article; zbMATH DE number 6971734