EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

doi:10.1016/S0252-9602(13)60015-6

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (2): 505-524.doi: 10.1016/S0252-9602(13)60015-6

EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

N. TATAR

King Fahd University of Petroleum and Minerals, Department of Mathematics &|Statistics, Dhahran 31261, Saudi Arabia

收稿日期:2011-11-21 修回日期:2012-08-27 出版日期:2013-03-20 发布日期:2013-03-20
基金资助:
The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through project No. IN111034.

EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

N. TATAR

King Fahd University of Petroleum and Minerals, Department of Mathematics &|Statistics, Dhahran 31261, Saudi Arabia

Received:2011-11-21 Revised:2012-08-27 Online:2013-03-20 Published:2013-03-20
Supported by:
The author is grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through project No. IN111034.

摘要/Abstract

摘要：

Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-known that the system is exponentially stable if the kernel in the memory term is sub-exponential. That is, if the product of the kernel with an exponential function is a summable function. In this article we address the questions: What if the kernel is tested against a different function (say Gamma) other than the exponential function? Would there still be stability? In the affirmative, what kind of decay rate we get? It is proved that for a non-decreasing function “Gamma” whose “logarithmic derivative” is decreasing to zero we have a decay of order Gamma to some power and in the case it decreases to a different value than zero then the decay is exponential.

关键词: Arbitrary decay, memory term, relaxation function, Timoshenko beam, vis-coelasticity

Abstract:

Key words: Arbitrary decay, memory term, relaxation function, Timoshenko beam, vis-coelasticity

中图分类号:

35L20

N. TATAR. EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM[J]. 数学物理学报(英文版), 2013, 33(2): 505-524.

N. TATAR. EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM[J]. Acta mathematica scientia,Series B, 2013, 33(2): 505-524.

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EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

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