Dynamic behavior of a one-dimensional thermoviscoelastic system

Jing Wang; Jun Min Wang

doi:10.1109/CCDC.2015.7162260

Dynamic behavior of a one-dimensional thermoviscoelastic system

Jing Wang, Jun Min Wang

School of Mathematics and Statistics

Hebei Finance University

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

Abstract

In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.

Original language	English
Title of host publication	Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2061-2066
Number of pages	6
ISBN (Electronic)	9781479970179
DOIs	https://doi.org/10.1109/CCDC.2015.7162260
Publication status	Published - 17 Jul 2015
Event	27th Chinese Control and Decision Conference, CCDC 2015 - Qingdao, China Duration: 23 May 2015 → 25 May 2015

Publication series

Name	Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015

Conference

Conference	27th Chinese Control and Decision Conference, CCDC 2015
Country/Territory	China
City	Qingdao
Period	23/05/15 → 25/05/15

Keywords

Asymptotic analysis
Riesz basis
Stability
Thermoviscoelastic system

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10.1109/CCDC.2015.7162260

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Wang, J., & Wang, J. M. (2015). Dynamic behavior of a one-dimensional thermoviscoelastic system. In Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015 (pp. 2061-2066). Article 7162260 (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCDC.2015.7162260

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title = "Dynamic behavior of a one-dimensional thermoviscoelastic system",

abstract = "In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.",

keywords = "Asymptotic analysis, Riesz basis, Stability, Thermoviscoelastic system",

author = "Jing Wang and Wang, {Jun Min}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 27th Chinese Control and Decision Conference, CCDC 2015 ; Conference date: 23-05-2015 Through 25-05-2015",

year = "2015",

month = jul,

day = "17",

doi = "10.1109/CCDC.2015.7162260",

language = "English",

series = "Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015",

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

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booktitle = "Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015",

address = "United States",

}

Wang, J & Wang, JM 2015, Dynamic behavior of a one-dimensional thermoviscoelastic system. in Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015., 7162260, Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 2061-2066, 27th Chinese Control and Decision Conference, CCDC 2015, Qingdao, China, 23/05/15. https://doi.org/10.1109/CCDC.2015.7162260

Dynamic behavior of a one-dimensional thermoviscoelastic system. / Wang, Jing; Wang, Jun Min.
Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2061-2066 7162260 (Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015).

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

TY - GEN

T1 - Dynamic behavior of a one-dimensional thermoviscoelastic system

AU - Wang, Jing

AU - Wang, Jun Min

PY - 2015/7/17

Y1 - 2015/7/17

N2 - In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.

AB - In this paper, we study the dynamic behavior of a one-dimensional linear thermoviscoelastic system with Dirichlet boundary conditions. A remarkable characteristic is that the system operator is not of compact resolvent. Using the asymptotic analysis technique, it is shown that there are three branches of eigenvalues: two of them are along the negative real axis approaching-∞ and another branch, distributing on the negative real axis, converges to a negative real point which is the unique continuous spectrum. Moreover, the set of generalized eigenfunctions forms a Riesz basis for the energy state space. Consequently, the spectrum-determined growth condition holds true, and an exponential stability is concluded. Finally, some numerical simulations are presented.

KW - Asymptotic analysis

KW - Riesz basis

KW - Stability

KW - Thermoviscoelastic system

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U2 - 10.1109/CCDC.2015.7162260

DO - 10.1109/CCDC.2015.7162260

M3 - Conference contribution

AN - SCOPUS:84945568277

T3 - Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015

SP - 2061

EP - 2066

BT - Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 27th Chinese Control and Decision Conference, CCDC 2015

Y2 - 23 May 2015 through 25 May 2015

ER -

Dynamic behavior of a one-dimensional thermoviscoelastic system

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