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
To analyze the stability problem of spatial beam structure more accurately, a spatial cubic spline geometric nonlinear beam dement was proposed considering the seeond-order effect. The deformation field was built with...To analyze the stability problem of spatial beam structure more accurately, a spatial cubic spline geometric nonlinear beam dement was proposed considering the seeond-order effect. The deformation field was built with cubic spline function, and its curvature degree of freedom （DOF） was eliminated by static condensation method. Then we got the geometric nonlinear stiffness matrix of the new spatial two.node Euler-Bernouili beam dement. Several examples proved calculation accuracy of the critical load by meshing a bar to one element using the method of this paper was equivalent to mesh a bar to 3 or 4 traditional nonlinear beam dements.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To analyze the stability problem of spatial beam structure more accurately, a spatial cubic spline geometric nonlinear beam dement was proposed considering the seeond-order effect. The deformation field was built with cubic spline function, and its curvature degree of freedom （DOF） was eliminated by static condensation method. Then we got the geometric nonlinear stiffness matrix of the new spatial two.node Euler-Bernouili beam dement. Several examples proved calculation accuracy of the critical load by meshing a bar to one element using the method of this paper was equivalent to mesh a bar to 3 or 4 traditional nonlinear beam dements.
