EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM

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

Abstract

Abstract:

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.

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

CLC Number:

35L20

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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