This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial mul...This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t →∞.展开更多
Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop...Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop system. Then by using the energy perturbed method, it is proved that the vibration of the beam under the proposed control actions decays asymptotically or exponentially as t →∞.展开更多
基金This research is supported by the National Science Foundation of China under Grant Nos. 10671166 and 60673101.
文摘This paper studies the stabilization problem of uniform Euler-Bernoulli beam with a nonlinear locally distributed feedback control. By virtue of nonlinear semigroup theory, energy-perturbed approach and polynomial multiplier skill, the authors show that, corresponding to the different values of the parameters involved in the nonlinear locally distributed feedback control, the energy of the beam under the proposed feedback decays exponentially or in negative power of time t as t →∞.
文摘Nonlinear boundary feedback control to a Timoshenko beam is studied. Under some nonlinear boundary feedback controls, the nonlinear semi group theory is used to show the well posedness for the correspnding closed loop system. Then by using the energy perturbed method, it is proved that the vibration of the beam under the proposed control actions decays asymptotically or exponentially as t →∞.
