Journal ArticleDOI
Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity
TLDR
In this article, a two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated, where the transport speed is assumed to be a constant mean speed with small harmonic variations.Abstract:
Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton's second law. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. Closed-form solutions for the amplitude of the vibration and the existence conditions of nontrivial steady-state response in two-to-one parametric resonance are obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Lyapunov's linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions for two-to-one parametric resonance. Some numerical examples highlighting the effects of the related parameters on the stability conditions are presented.read more
Citations
More filters
Journal ArticleDOI
Analysis and Control of Transverse Vibrations of Axially Moving Strings
TL;DR: In this article, the authors present the governing equations with large amplitude, and review progress on discretized or direct approximate analytical analyses and numerical approaches based on the Galerkin method or the finite difference method.
Journal ArticleDOI
Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models
Li-Qun Chen,Xiao-Dong Yang +1 more
TL;DR: In this article, principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed, and closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms.
Journal ArticleDOI
Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations
Mehmet Pakdemirli,H. R. Öz +1 more
TL;DR: In this paper, the transverse vibrations of simply supported axially moving Euler-Bernoulli beams are investigated using the method of multiple scales, a perturbation technique.
Journal ArticleDOI
Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt
M. H. Yao,Wei Zhang,Jean W. Zu +2 more
TL;DR: In this article, the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear, nonplanar oscillations of the parametrically excited viscoelastic moving belt using an extended Melnikov method in the resonant case were investigated.
Journal ArticleDOI
Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics
TL;DR: In this paper, the eigenvalue problem for transverse vibrations of axially moving strings is solved using the Hamiltonian dynamics, and the non-singular modal functions are obtained through a linear, symplectic eigen value analysis.
References
More filters
Journal ArticleDOI
Classical Vibration Analysis of Axially Moving Continua
J. A. Wickert,C. D. Mote +1 more
TL;DR: In this article, the equations of motion are cast in a canonical state space form defined by one symmetric and one skew-symmetric differential operator, and the eigenfunctions are orthogonal with respect to each operator.
Journal ArticleDOI
Current research on the vibration and stability of axially-moving materials
J. A Wicker,C. D. Mote +1 more
Journal ArticleDOI
Vibrations of belts and belt drives
TL;DR: In this paper, the effects of initial tension, transport velocity, bending rigidity, support flexibility, large displacements and belt and pulley imperfections are discussed, and influence of several complicating factors are mentioned.
Journal ArticleDOI
Stability analysis of an axially accelerating string
Mehmet Pakdemirli,A. G. Ulsoy +1 more
TL;DR: In this paper, the authors investigated the dynamic response of an axially accelerating string, where the time dependent velocity is assumed to vary harmonically about a constant mean velocity, and they found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequencies are close to the sum of any two natural frequencies, but no instabilities are detected up to the first order of perturbation.
Journal ArticleDOI
Transverse Vibration of an Axially Accelerating String
TL;DR: In this paper, the transverse vibration of an axially accelerating string is investigated using Hamilton's principle, and the resulting partial differential equations are discretized using Galerkin's method.