On the Vibrations of an Axially Moving String With a Time-Dependent Velocity

Rajab A. Malookani; Wim van Horssen

doi:10.1115/IMECE2015-50452

On the Vibrations of an Axially Moving String With a Time-Dependent Velocity

Mathematical Physics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

Abstract

The transverse vibrations of an axially moving string with a time-varying speed is studied in this paper. The governing equations of motion describing an axially moving string is analyzed using two different techniques. At first, the initial-boundary value problem is discretized using the Fourier sine series, and then the two timescales perturbation method is employed in search of infinite mode approximate solutions. Secondly, a new approach based on the two timescales perturbation method and the method of characteristics is used. It is found that there are infinitely many values of the velocity fluctuation frequency yielding infinitely many resonance conditions in the system. The response of the system with harmonically varying velocity function is computed for particular harmonic initial conditions.

Original language	English
Title of host publication	Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015
Publisher	ASME
Pages	1-10
Number of pages	10
Volume	4B
ISBN (Print)	978-0-7918-5740-3
DOIs	https://doi.org/10.1115/IMECE2015-50452
Publication status	Published - 2015
Event	ASME 2015 International Mechanical Engineering Congress and Exposition - Houston, United States Duration: 13 Nov 2015 → 19 Nov 2015

Conference

Conference	ASME 2015 International Mechanical Engineering Congress and Exposition
Country/Territory	United States
City	Houston
Period	13/11/15 → 19/11/15

Keywords

String
Vibration

Access to Document

10.1115/IMECE2015-50452

Cite this

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title = "On the Vibrations of an Axially Moving String With a Time-Dependent Velocity",

abstract = "The transverse vibrations of an axially moving string with a time-varying speed is studied in this paper. The governing equations of motion describing an axially moving string is analyzed using two different techniques. At first, the initial-boundary value problem is discretized using the Fourier sine series, and then the two timescales perturbation method is employed in search of infinite mode approximate solutions. Secondly, a new approach based on the two timescales perturbation method and the method of characteristics is used. It is found that there are infinitely many values of the velocity fluctuation frequency yielding infinitely many resonance conditions in the system. The response of the system with harmonically varying velocity function is computed for particular harmonic initial conditions.",

keywords = "String, Vibration",

author = "Malookani, {Rajab A.} and {van Horssen}, Wim",

year = "2015",

doi = "10.1115/IMECE2015-50452",

language = "English",

isbn = "978-0-7918-5740-3",

volume = "4B",

pages = "1--10",

booktitle = "Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015",

publisher = "ASME",

address = "United States",

note = "ASME 2015 International Mechanical Engineering Congress and Exposition ; Conference date: 13-11-2015 Through 19-11-2015",

}

Malookani, RA & van Horssen, W 2015, On the Vibrations of an Axially Moving String With a Time-Dependent Velocity. in Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015. vol. 4B, ASME, pp. 1-10, ASME 2015 International Mechanical Engineering Congress and Exposition, Houston, United States, 13/11/15. https://doi.org/10.1115/IMECE2015-50452

On the Vibrations of an Axially Moving String With a Time-Dependent Velocity. / Malookani, Rajab A.; van Horssen, Wim.
Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015. Vol. 4B ASME, 2015. p. 1-10.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - On the Vibrations of an Axially Moving String With a Time-Dependent Velocity

AU - Malookani, Rajab A.

AU - van Horssen, Wim

PY - 2015

Y1 - 2015

N2 - The transverse vibrations of an axially moving string with a time-varying speed is studied in this paper. The governing equations of motion describing an axially moving string is analyzed using two different techniques. At first, the initial-boundary value problem is discretized using the Fourier sine series, and then the two timescales perturbation method is employed in search of infinite mode approximate solutions. Secondly, a new approach based on the two timescales perturbation method and the method of characteristics is used. It is found that there are infinitely many values of the velocity fluctuation frequency yielding infinitely many resonance conditions in the system. The response of the system with harmonically varying velocity function is computed for particular harmonic initial conditions.

AB - The transverse vibrations of an axially moving string with a time-varying speed is studied in this paper. The governing equations of motion describing an axially moving string is analyzed using two different techniques. At first, the initial-boundary value problem is discretized using the Fourier sine series, and then the two timescales perturbation method is employed in search of infinite mode approximate solutions. Secondly, a new approach based on the two timescales perturbation method and the method of characteristics is used. It is found that there are infinitely many values of the velocity fluctuation frequency yielding infinitely many resonance conditions in the system. The response of the system with harmonically varying velocity function is computed for particular harmonic initial conditions.

KW - String

KW - Vibration

U2 - 10.1115/IMECE2015-50452

DO - 10.1115/IMECE2015-50452

M3 - Conference contribution

SN - 978-0-7918-5740-3

VL - 4B

SP - 1

EP - 10

BT - Proceedings of the ASME 2015 International Mechanical Engineering Congress & Exposition IMECE2015

PB - ASME

T2 - ASME 2015 International Mechanical Engineering Congress and Exposition

Y2 - 13 November 2015 through 19 November 2015

ER -

On the Vibrations of an Axially Moving String With a Time-Dependent Velocity

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Keywords

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