Computing the dynamic response of an axially moving continuum

Čepon, Gregor; Boltežar, Miha

doi:10.1016/j.jsv.2006.08.014

Cited by 28 publications

(13 citation statements)

References 20 publications

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“…Luo [26] studied the buckling stability and post-buckling chaos of an axially moving plate by Galerkin method and then numerical method. According to the report byČepon and Boltežar [27], the finite difference method is efficient and effective in the dynamical study of forced axially moving continuum.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton's second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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“…where φ(x) = sin(iπx/l) describes the effect of the ith eigenvalue of the stationary beam, and q i (t) represents the generalized transverse displacement (Cepon & Boltezar, 2007). Utilizing boundary condition (3) and substituting Eq.…”

Section: Problem Formulationmentioning

confidence: 99%

“…In these researches, the transverse displacement of an axially moving beam was expanded into a Fourier series (a sine series is a good candidate), and the Galerkin method was applied to reduce the partial differential equation (PDE) that governs the transverse motion into a set of ordinary differential equations (ODEs), which is a dimensional discrete model. The discrete models obtained by using the Galerkin method were compared with results obtained by using other methods (e.g., multiple time scales and Laplace transform) as well as experimental results, and good agreements were shown (Pellicano & Vestroni, 2002;Pellicano, Gatellani, & Fregolent, 2004;Cepon & Boltezar, 2007).…”

Section: Introductionmentioning

confidence: 98%

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Transverse Vibration Control of Axially Moving Beams by Regulation of Axial Velocity

Nguyen

Hong

2011

IFAC Proceedings Volumes

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In this paper, a novel control algorithm for suppression of the transverse vibration of an axially moving system is presented. The principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving system so as to track a profile according to which the vibration energy decays most quickly. The optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations (ODEs). For control design purposes, these ODEs are rewritten into statespace equations. The vibration energy of the axially moving beam is represented by the quadratic form of the state variables. In the optimal control problem, the cost function modified from the vibration energy function is subject to the constraints on the state variables, and the axial transport velocity is considered as a control input. Numerical simulations are performed to confirm the effectiveness of the proposed control algorithm.

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“…Sze et al [14] employed Galerkin method to discretize the governing equations of an axially moving beam and formulated the incremental harmonic balance method for non-linear vibration. Cepon and Boltezar [15] applied an approximate Gelerkin finite element method to solve the initial-/boundary-value problem of a viscously damped and axially moving beam with pre-tension. It was shown that for certain values of the parameters, especially at high velocities, Galerkin method using stationary string eigenfunctions would give a poor prediction of the dynamic response.…”

Section: Introductionmentioning

confidence: 99%

Vibration and stability of an axially moving Rayleigh beam

Chang¹,

Lin

Huang³

et al. 2010

Applied Mathematical Modelling

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a b s t r a c tIn this paper, the vibration and stability of an axially moving beam is investigated. The finite element method with variable-domain elements is used to derive the equations of motion of an axially moving beam based on Rayleigh beam theory. Two kinds of axial motions including constant-speed extension deployment and back-and-forth periodical motion are considered. The vibration and stability of beams with these motions are investigated. For vibration analysis, direct time numerical integration, based on a Runge-Kutta algorithm, is used. For stability analysis of a beam with constant-speed axial extension deployment, eigenvalues of equations of motion are obtained to determine its stability, while Floquet theory is employed to investigate the stability of the beam with back-andforth periodical axial motion. The effects of oscillation amplitude and frequency of periodical axial movement on the stability of the beam are discussed from the stability chart. Time histories are established to confirm the results from Floquet theory.

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Computing the dynamic response of an axially moving continuum

Cited by 28 publications

References 20 publications

Dynamical analysis of axially moving plate by finite difference method

Dynamical analysis of axially moving plate by finite difference method

Transverse Vibration Control of Axially Moving Beams by Regulation of Axial Velocity

Vibration and stability of an axially moving Rayleigh beam

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