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A reflected wave superposition method for vibration and energy of a travelling string

A reflected wave superposition method for vibration and energy of a travelling string
A reflected wave superposition method for vibration and energy of a travelling string
This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics.
0022-460X
40-57
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Luo, Q.
15d65bb0-d13e-4c60-982c-e77f0d5c5377
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Luo, Q.
15d65bb0-d13e-4c60-982c-e77f0d5c5377
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c

Chen, E.W., Luo, Q., Ferguson, N.S. and Lu, Y.M. (2017) A reflected wave superposition method for vibration and energy of a travelling string. Journal of Sound and Vibration, 400, 40-57. (doi:10.1016/j.jsv.2017.03.046).

Record type: Article

Abstract

This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics.

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Reflected waves manuscript 2_3_17 - Accepted Manuscript
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Accepted/In Press date: 31 March 2017
e-pub ahead of print date: 20 April 2017
Published date: 21 July 2017
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 410748
URI: https://eprints.soton.ac.uk/id/eprint/410748
ISSN: 0022-460X
PURE UUID: 879773a4-3a12-47f3-b80f-3818c0bae2fa
ORCID for N.S. Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

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Date deposited: 09 Jun 2017 09:33
Last modified: 14 Mar 2019 06:00

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