On the transversal vibrations of an axially moving continuum with a time-varying velocity: Transient from string to beam behavior

Пономарева, С. В.; Horssen, Wim T. van

doi:10.1016/j.jsv.2009.03.038

Cited by 33 publications

(4 citation statements)

References 12 publications

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“…Inserting Eqs. (22)(23)(24) into Eqs. (21a-21b), and equating like powers of ε, and omitting the higher terms of ε in the resulting equations, one obtains a general form for any power of ε as follows:…”

Section: Analytical Solutions: Perturbation Analysismentioning

confidence: 99%

“…22 Pasin analyzed periodically reciprocating motion in axial direction, 23 and Ponomareva and van Horssen studied it in stretched case. 24 When solving axially moving beam problem, different solution methods have been used: the complex modal method 25 and the variation method, 26 the method of multiple scales, and the method of matched asymptotic expansions. 27 Axially moving beams have been analyzed by subjecting it to a transverse force, 28 by having small bending stiffness, 29 and by considering multiple concentrated masses on the beam.…”

Section: Introductionmentioning

confidence: 99%

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Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

Sarıgül¹

2019

The International Journal of Acoustics and Vibration

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Nonlinear transverse vibrations of axially moving beams with multiple cracks is handled studied. Assuming that the beam moves with mean velocity having harmonically variation, influence of the edge crack on the moving continua are investigated in this study. Due to existence of the crack in the transverse direction, the healthily beam is divided into parts. The translational and rotational springs are replaced between these parts so that high stressed regions around the crack tips are redefined with the springs' energies. Thus, the problem is converted to an axially moving spring-beam system. The equations of motion and its corresponding conditions are obtained by means of the Hamilton Principle. In numerical analysis, the natural frequencies and responses of the spring-beam system are investigated for principal parametric resonance in detail. Some important results are obtained; the natural frequencies decreases with increasing crack depth. In case of the beam travelling with high velocities, the effects of crack's depth on natural frequencies seems to be vanished.

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Section: Analytical Solutions: Perturbation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

Sarıgül¹

2019

The International Journal of Acoustics and Vibration

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“…Based on different model systems, the dynamics of axially moving continua has been studied extensively, and many results that reflect the corresponding physical mechanisms from different aspects have been documented (Wickert and Mote, 1990;Chung et al, 2001;Chen et al, 2002;Pellicano and Vestroni, 2002;Horssen, 2003;Horssen and Ponomareva, 2005;Ha et al, 2007;Ghayesh, 2008Ghayesh, , 2010Ghayesh, , 2011Ghayesh, , 2012Koivurova, 2009;Ponomareva and Horssen, 2009;Ghayesh et al, 2012;Yang and Fang, 2013). In particular, some researchers have shown that the truncation method for string-like problems may lead to wrong results (Suweken and Horssen, 2003a, 2003band 2003cPonomareva and Horssen, 2007).…”

Section: Introductionmentioning

confidence: 99%

Experimental study of the nonlinear characteristics of an axially moving string

Xia

2014

Journal of Vibration and Control

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This paper presents an experimental study of the nonlinear characteristics of an axially moving string. An experimental system with a simple configuration, which is similar to a practical application, was built. Two laser sensors were used to monitor the vertical and horizontal vibrations of the moving string under different conditions. Using the Hilbert-Huang transform method, the detailed results of a typical measured data series, which include intrinsic mode decomposition, Hilbert spectrum and marginal spectrum, are introduced. For comparison, marginal spectra for almost all test cases are also given. Based on the results, several observed nonlinear phenomena, which include whirling motion, resonances, quasiperiodical and a beating motion, torus doublings and one chaotic motion, are presented. The quantitative nonlinear vibrating details and the observed rich behaviors help explain the great complexity of a single moving string.

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“…Marynowski and co-investigators [13,14] introduced several energy dissipation mechanisms into the mathematical models of the system. Van Horssen and co-investigators [15][16][17] investigated the system dynamics using a discretization perturbation technique. Zhu and Zheng [18] examined the effect of variable length on the dynamics of an axially translating string.…”

Section: Introductionmentioning

confidence: 99%

Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

Kazemirad

Ghayesh

Amabili

2013

Shock and Vibration

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Abstract. The thermo-mechanical nonlinear vibrations and stability of a hinged-hinged axially moving beam, additionally supported by a nonlinear spring-mass support are examined via two numerical techniques. The system is subjected to a transverse harmonic excitation force as well as a thermal loading. Hamilton's principle is employed to derive the equations of motion; it is discretized into a multi-degree-freedom system by means of the Galerkin method. The steady state resonant response of the system for both cases with and without an internal resonance between the first two modes is examined via the pseudo-arclength continuation technique. In the second method, direct time integration is employed to construct bifurcation diagrams of Poincaré maps of the system.

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On the transversal vibrations of an axially moving continuum with a time-varying velocity: Transient from string to beam behavior

Cited by 33 publications

References 12 publications

Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

Experimental study of the nonlinear characteristics of an axially moving string

Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

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