Frequency analysis of a wave equation with Kelvin-Voigt damping

Bao Zhu Guo; Jun Min Wang; Guo Dong Zhang

doi:10.1109/CDC.2009.5399989

Frequency analysis of a wave equation with Kelvin-Voigt damping

Bao Zhu Guo^*, Jun Min Wang, Guo Dong Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite algebraic multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4471-4476
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399989
Publication status	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	15/12/09 → 18/12/09

Access to Document

10.1109/CDC.2009.5399989

Cite this

Guo, B. Z., Wang, J. M., & Zhang, G. D. (2009). Frequency analysis of a wave equation with Kelvin-Voigt damping. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 4471-4476). Article 5399989 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399989

Guo, Bao Zhu ; Wang, Jun Min ; Zhang, Guo Dong. / Frequency analysis of a wave equation with Kelvin-Voigt damping. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 4471-4476 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{07290e4ad55a4e338d7763c6a638d8a8,

title = "Frequency analysis of a wave equation with Kelvin-Voigt damping",

abstract = "A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite algebraic multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.",

author = "Guo, {Bao Zhu} and Wang, {Jun Min} and Zhang, {Guo Dong}",

year = "2009",

doi = "10.1109/CDC.2009.5399989",

language = "English",

isbn = "9781424438716",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4471--4476",

booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

address = "United States",

note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

}

Guo, BZ, Wang, JM & Zhang, GD 2009, Frequency analysis of a wave equation with Kelvin-Voigt damping. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399989, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4471-4476, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 15/12/09. https://doi.org/10.1109/CDC.2009.5399989

Frequency analysis of a wave equation with Kelvin-Voigt damping. / Guo, Bao Zhu; Wang, Jun Min; Zhang, Guo Dong.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 4471-4476 5399989 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Guo, Bao Zhu

AU - Wang, Jun Min

AU - Zhang, Guo Dong

PY - 2009

Y1 - 2009

N2 - A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite algebraic multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.

AB - A vibrating system with some kind of internal damping represents a distributed or passive control. In this article, a wave equation with clamped boundary conditions and internal Kelvin-Voigt damping is considered. It is shown that the spectrum of system operator is composed of two parts: point spectrum and continuous spectrum. The point spectrum is consist of isolated eigenvalues of finite algebraic multiplicity, and the continuous spectrum is an interval on the left real axis. The asymptotic behavior of eigenvalues is presented.

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U2 - 10.1109/CDC.2009.5399989

DO - 10.1109/CDC.2009.5399989

M3 - Conference contribution

AN - SCOPUS:77950830650

SN - 9781424438716

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

Y2 - 15 December 2009 through 18 December 2009

ER -

Guo BZ, Wang JM, Zhang GD. Frequency analysis of a wave equation with Kelvin-Voigt damping. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 4471-4476. 5399989. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399989

Frequency analysis of a wave equation with Kelvin-Voigt damping

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