Vibrations of an Axially Moving Beam With Time-Dependent Velocity

Pakdemi̇rli̇, Mehmet

doi:10.1006/jsvi.1999.2247

Cited by 218 publications

(73 citation statements)

References 26 publications

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“…In fact in [8][9][10][11] the equations (1) or (2) have been studied, where V (t) as given by (3) belongs to cases that have been studied in [8][9][10][11]. To find approximations of the displacement of the belt in vertical direction the authors use in [8][9][10][11] the method eigenfunction expansions, the Galerkin truncation method, and the multiple-timescales perturbation method as for instance described in [12,13]. To apply the method of eigenfunction expansions, special attention has to be paid to terms involving u x and u xt in (1) or (2).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Recently in a series of papers [8][9][10][11] several authors considered the vibrations of belts moving with time-dependent velocities and the vibrations of tensioned pipes conveying fluid with timedependent velocities. In fact in [8][9][10][11] the equations (1) or (2) have been studied, where V (t) as given by (3) belongs to cases that have been studied in [8][9][10][11]. To find approximations of the displacement of the belt in vertical direction the authors use in [8][9][10][11] the method eigenfunction expansions, the Galerkin truncation method, and the multiple-timescales perturbation method as for instance described in [12,13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

Suweken

Horssen

2003

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

Suweken

Horssen

2003

Journal of Sound and Vibration

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“…(13) [22] commented the stable and unstable regions on similar diagrams, depicting the area between two surfaces as unstable region, while the areas outside the two surfaces should be stable. …”

Section: Amplitudes Of Response Of the Travelling Beam At Principal Pmentioning

confidence: 99%

Influence of the longitudinal displacement on the nonlinear principal parametric resonance of the woodworking bandsaw

2017

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Original scientific paper The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice. Keywords: hybrid boundary conditions; method of multiple scales; numerical examples; principal parametric resonance; travelling Timoshenko beam Utjecaj uzdužnog pomaka na nelinearne glavne parametarske rezonancije tračne pileIzvorni znanstveni članak U radu su istražene poprečne vibracije aksijalno pomične Timoshenkove grede, kao podesnog modela za matematičko modeliranje tračnih pila. Posebno je obrađen utjecaj aksijalnog pomaka koji je, za razliku od većine modela koji se susreću u literaturi, uveden preko integro-parcijalne diferencijalne jednadžbe. Također su izvedeni izrazi za forme vibriranja za slučaj hibridnih oslonaca s različitim krutostima torzijskih opruga u točkama oslonaca. Ispitivan je utjecaj srednje brzine gibanja grede kao i aksijalnog naprezanja na vlastite frekvencije i oblike vibriranja. Razvijen je i nelinearni model na temelju kojega su izračunati amplitudni odzivi nelinearnih ravnomjernih vibracija za slučaj parametarske rezonancije. Izrađeno programsko rješenje testirano je na određenom broju ranije poznatih primjera. Iznijeta teorijska razmatranja, uz pomoć programskog rješenja, poslužila su i za analizu jednog od dostupnih primjera iz industrijske prakse.

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“…For example, Pakdemirli and co-workers [6][7][8][9] examined the vibrations of axially moving strings and beams by means of some perturbation techniques such as the method of multiple timescales and matched asymptotic expansion. Chen and co-workers [10][11][12] employed both analytical and numerical techniques to examine the dynamics of axially moving systems.…”

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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Vibrations of an Axially Moving Beam With Time-Dependent Velocity

Cited by 218 publications

References 26 publications

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

Influence of the longitudinal displacement on the nonlinear principal parametric resonance of the woodworking bandsaw

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

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