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A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string

A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string
A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string
The finite length translating tensioned string model with mixed boundary conditions is considered in order to study the exchange of vibrational energy during reflection process in this paper. The boundary conditions are respectively at one end a spring-dashpot and the other a fixed boundary, which is one kind of mixed boundary conditions. An analytical solution and energy expressions for the propagating wave are presented, which uses a reflected wave superposition method. Firstly, the cycle of boundary reflection for strings is provided. To simplify the process for obtaining the response, each cycle is divided into three time intervals. Applying D’Alembert’s principle and the reflection properties, expressions for the reflected waves under these mixed boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals. 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 these spring-dashpot and fixed boundary conditions are obtained by using the analytical solution and the properties of vibrational energy exchange as a function of the translational velocity, the boundaries and level of damping are discussed.
energy exchange, travelling string, nonclassical boundaries, reflection properties, wave superposition
0888-3270
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Yuan, J.F.
17d012ed-8064-4916-83af-84056ca657e4
Ferguson, Neil
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Zhang, K.
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Zhu, W.D.
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Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c
Wei, H.Z.
bfd4ba0b-b6bf-4851-82f1-db02941a6c05
Chen, E.W.
bacac18f-2823-44ea-b8b2-bd61b1b3b94b
Yuan, J.F.
17d012ed-8064-4916-83af-84056ca657e4
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Zhang, K.
f6b44da1-e674-42f7-bb42-027f5b143266
Zhu, W.D.
b8244fb0-9587-46d5-9589-0ce77cac4fe2
Lu, Y.M.
db9b219e-d19f-4246-9860-04b103a87e4c
Wei, H.Z.
bfd4ba0b-b6bf-4851-82f1-db02941a6c05

Chen, E.W., Yuan, J.F., Ferguson, Neil, Zhang, K., Zhu, W.D., Lu, Y.M. and Wei, H.Z. (2020) A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string. Mechanical Systems and Signal Processing. (In Press)

Record type: Article

Abstract

The finite length translating tensioned string model with mixed boundary conditions is considered in order to study the exchange of vibrational energy during reflection process in this paper. The boundary conditions are respectively at one end a spring-dashpot and the other a fixed boundary, which is one kind of mixed boundary conditions. An analytical solution and energy expressions for the propagating wave are presented, which uses a reflected wave superposition method. Firstly, the cycle of boundary reflection for strings is provided. To simplify the process for obtaining the response, each cycle is divided into three time intervals. Applying D’Alembert’s principle and the reflection properties, expressions for the reflected waves under these mixed boundary conditions are derived. Then, the vibrational response of the axially translating string is solved for three time intervals. 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 these spring-dashpot and fixed boundary conditions are obtained by using the analytical solution and the properties of vibrational energy exchange as a function of the translational velocity, the boundaries and level of damping are discussed.

Text
MSSP20-758R1-1 edited - Accepted Manuscript
Restricted to Repository staff only until 1 September 2022.
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Accepted/In Press date: 1 September 2020
Keywords: energy exchange, travelling string, nonclassical boundaries, reflection properties, wave superposition

Identifiers

Local EPrints ID: 443580
URI: http://eprints.soton.ac.uk/id/eprint/443580
ISSN: 0888-3270
PURE UUID: 77a42d2a-1cbe-4a4b-817e-391c817de268
ORCID for Neil Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

Catalogue record

Date deposited: 03 Sep 2020 01:47
Last modified: 13 Dec 2021 02:32

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Contributors

Author: E.W. Chen
Author: J.F. Yuan
Author: Neil Ferguson ORCID iD
Author: K. Zhang
Author: W.D. Zhu
Author: Y.M. Lu
Author: H.Z. Wei

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