EXPONENTIAL DECAY FOR A VISCOELASTICALLY DAMPED TIMOSHENKO BEAM  

作　　者：N. TATAR 

机构地区：[1]King Fahd University of Petroleum and Minerals,Department of Mathematics & Statistics,Dhahran 31261,Saudi Arabia

出　　处：《Acta Mathematica Scientia》2013年第2期505-524,共20页数学物理学报（B辑英文版）

基　　金：the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through project No. IN111034

摘　　要：Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn 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.Of concern is a viscoelastic beam modelled using the Timoshenko theory. It is well-kimwn 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 

分 类 号：O174[理学—数学]