An analytical wave solution for the vibrational response and energy of an axially translating string in any propagation cycle
An analytical wave solution for the vibrational response and energy of an axially translating string in any propagation cycle
An axially traveling string system, which is a kind of traveling material, attracts considerable attention owing to its broad applications. In this paper, an analytical wave solution for the vibration and energy of an axially traveling string with fixed and viscous damper (dashpot) boundaries in any propagation cycle is considered. Firstly, a novel recursive and simplified technique is proposed to expand the analytical solution for a traveling string to any propagation cycle, which was limited to only one propagation cycle due to complexity in previous work. As a kind of analytical solution, the traveling wave method has more accuracy and efficiency compared to numerical methods. Secondly, different from the previous result, the modified Hamilton’s principle is applied to the derivation of the dashpot boundary condition for the mass changing of the traveling string. Following the pipeline hydrodynamics theory, the energy gradient for the ‘control volume’ and the ‘system’ of traveling string are accurately obtained, respectively. Thirdly, from the point of view of vibration suppression, the optimal damping at the right end of the string is defined and the optimal damping value is derived, which is of considerable practical interest in vibration suppression at boundaries for axially traveling materials.
analytical, energy, traveling string, vibration suppression
He, Yuteng
b7f7ab54-7de2-4aa6-a6cd-30466bd1d7ee
Chen, Enwei
808a82ee-6f26-4047-bd12-9e6a1e55c6fa
Zhu, Weidong
0192832e-6e65-4faa-aa48-f6fde5aedf94
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Wu, Yuanfeng
6ee200c9-07f2-417b-b198-71cebbc82d15
Lu, Yimin
596a6e39-b819-4c9d-927a-74dd43245a11
He, Yuteng
b7f7ab54-7de2-4aa6-a6cd-30466bd1d7ee
Chen, Enwei
808a82ee-6f26-4047-bd12-9e6a1e55c6fa
Zhu, Weidong
0192832e-6e65-4faa-aa48-f6fde5aedf94
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Wu, Yuanfeng
6ee200c9-07f2-417b-b198-71cebbc82d15
Lu, Yimin
596a6e39-b819-4c9d-927a-74dd43245a11
He, Yuteng, Chen, Enwei, Zhu, Weidong, Ferguson, Neil, Wu, Yuanfeng and Lu, Yimin
(2022)
An analytical wave solution for the vibrational response and energy of an axially translating string in any propagation cycle.
Elsevier, 181, [109507].
(doi:10.1016/j.ymssp.2022.109507).
Abstract
An axially traveling string system, which is a kind of traveling material, attracts considerable attention owing to its broad applications. In this paper, an analytical wave solution for the vibration and energy of an axially traveling string with fixed and viscous damper (dashpot) boundaries in any propagation cycle is considered. Firstly, a novel recursive and simplified technique is proposed to expand the analytical solution for a traveling string to any propagation cycle, which was limited to only one propagation cycle due to complexity in previous work. As a kind of analytical solution, the traveling wave method has more accuracy and efficiency compared to numerical methods. Secondly, different from the previous result, the modified Hamilton’s principle is applied to the derivation of the dashpot boundary condition for the mass changing of the traveling string. Following the pipeline hydrodynamics theory, the energy gradient for the ‘control volume’ and the ‘system’ of traveling string are accurately obtained, respectively. Thirdly, from the point of view of vibration suppression, the optimal damping at the right end of the string is defined and the optimal damping value is derived, which is of considerable practical interest in vibration suppression at boundaries for axially traveling materials.
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An analytical wave solution for the vibrational response and energy of an axially translating string in any pr
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Accepted/In Press date: 27 June 2022
e-pub ahead of print date: 15 July 2022
Keywords:
analytical, energy, traveling string, vibration suppression
Identifiers
Local EPrints ID: 468286
URI: http://eprints.soton.ac.uk/id/eprint/468286
PURE UUID: 293765a3-43cc-4f9c-a6a2-ca4d609b907b
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Date deposited: 09 Aug 2022 16:49
Last modified: 23 Feb 2023 02:32
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Contributors
Author:
Yuteng He
Author:
Enwei Chen
Author:
Weidong Zhu
Author:
Yuanfeng Wu
Author:
Yimin Lu
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