STABILIZATION OF NONUNIFORM TIMOSHENKOBEAM WITH COUPLED LOCALLY DISTRIBUTED FEEDBACKS

The stabilization problem of a nonuniform Timoshenko beam system With coupled locally distributed feedback controls is studied. First, by proving the uniqueness of the solution to the related ordinary differential equations, we establish the asymptotic decay of the energy corresponding to the closed loop system. Then, by virtue of piecewise multiplier method, we prove the exponential decay of the closed loop system.     

BOUNDARY STABILIZATION OF TIMOSHENKO BEAM

1. IntroductionConsider the following dynamic model of a Timoshenko beam with boundary feedbackcontrol: where a uniform beam of length F moves in w-x plane, p is the mass per unit length, w(x, t) thedeflection of the beam from its equilibrium and, W(x, t) the total rotatory angle of the beam atxs for whose precise physical meaning, see [1, 2]. In and EI are the mass moment of inertia andrigidity coefficient of the cross section, respectively, and K is the shear modulus of elajsticitv.The bou…     

ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT

1.IntroductionLetfibeaboundedopendomaininR"(n22)withsmoothboundaryr,u~u(s)betheoutwordnormalofrats.GivenavectorxoER",denotem(x)gx--xo(x6R"),Rgsup{lm(x)fjxCfi}.SetLndsupposer nrAI~0.Weconsiderthefollowingwaveequationonfiwithboundaryfeedback:whereK=(m'u)k,L…