In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total e...In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.展开更多
Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One ...Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.展开更多
文摘In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.
文摘Here we study a problem of stabilization of the flexural vibrations or transverse vibrations of a rectangular solar panel. The dynamics of vibrations is governed by the fourth order Euler-Bernoulli beam equation. One end of the panel is held by a rigid hub and other end is totally free. Due to attachment of the hub, its dynamics leads to a non-standard equation. The exponential stabilization of the whole system is achieved by applying an active boundary control force only on the rigid hub. The result of uniform stabilization is obtained by means of an explicit form of exponential energy decay estimate.
