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On the reflected wave superposition method for a travelling string with mixed boundary supports

On the reflected wave superposition method for a travelling string with mixed boundary supports
On the reflected wave superposition method for a travelling string with mixed boundary supports
An analytical vibration response in the time domain for an axially translating and laterally vibrating string with mixed boundary conditions is considered in this paper. The domain of the string is a constant, dependent upon the general initial conditions. The translating tensioned strings possess different types of mixed boundary conditions, such as fixed_dashpot, fixed_spring-dashpot, fixed_mass-spring-dashpot. An analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycle of boundary reflection for strings is provided, which is dependent upon the string length. Each cycle is divided into three time intervals according to the travelling speed and direction of the string. Applying D’Alembert’s principle and the reflection properties, expressions for the reflected waves under three different non-classical boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals by using a reflected wave superposition method. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-β method solution. The energy expressions for a travelling string with a fixed_dashpot boundary condition is obtained and the time domain curves for the total energy and the change of energy at the boundaries are given.
0022-460X
129-146
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Zhang, K.
f6b44da1-e674-42f7-bb42-027f5b143266
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Wang, J.
53d8d8bd-3c17-406e-9acf-961cc86b9a00
Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Zhang, K.
f6b44da1-e674-42f7-bb42-027f5b143266
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Wang, J.
53d8d8bd-3c17-406e-9acf-961cc86b9a00
Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c

Chen, E.W., Zhang, K., Ferguson, N.S., Wang, J. and Lu, Y.M. (2019) On the reflected wave superposition method for a travelling string with mixed boundary supports. Journal of Sound and Vibration, 440, 129-146. (doi:10.1016/j.jsv.2018.10.001).

Record type: Article

Abstract

An analytical vibration response in the time domain for an axially translating and laterally vibrating string with mixed boundary conditions is considered in this paper. The domain of the string is a constant, dependent upon the general initial conditions. The translating tensioned strings possess different types of mixed boundary conditions, such as fixed_dashpot, fixed_spring-dashpot, fixed_mass-spring-dashpot. An analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycle of boundary reflection for strings is provided, which is dependent upon the string length. Each cycle is divided into three time intervals according to the travelling speed and direction of the string. Applying D’Alembert’s principle and the reflection properties, expressions for the reflected waves under three different non-classical boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals by using a reflected wave superposition method. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-β method solution. The energy expressions for a travelling string with a fixed_dashpot boundary condition is obtained and the time domain curves for the total energy and the change of energy at the boundaries are given.

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2018.08.31 JSV manuscript_nsf_Pure - Accepted Manuscript
Restricted to Repository staff only until 15 October 2019.
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Accepted/In Press date: 1 October 2018
e-pub ahead of print date: 15 October 2018
Published date: 3 February 2019

Identifiers

Local EPrints ID: 425304
URI: https://eprints.soton.ac.uk/id/eprint/425304
ISSN: 0022-460X
PURE UUID: dd25ad73-c5c8-460d-8af2-acf588379029
ORCID for N.S. Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

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Date deposited: 12 Oct 2018 16:30
Last modified: 03 Apr 2019 00:38

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Contributors

Author: E.W. Chen
Author: K. Zhang
Author: N.S. Ferguson ORCID iD
Author: J. Wang
Author: Y.M. Lu

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