Exponential Stability for a Nonlinear Timoshenko System with Distributed Delay

Abstract

This paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with distributed delay time. The distributed delay is defined on feedback term associated to the equation for rotation angle. Under suitable assumptions on the data, we establish the exponential stability of the system under the usual equal wave speeds assumption.

Polynomial stability of nonlinear Timoshenko system with distributed delay-time

“…In the case where the speeds are nonequal, they established a polynomial decay estimate. System (1.1) was recently investigated by Bouzettouta et al [4] and they proved an exponential decay result of the energy when (1.6) holds, in this paper our goal is to complete their study for the case of non equal wave speeds.…”

Energy decay of one-dimensional thermoelastic bresse system with distributed neutral delay and a second sound

“…The Bresse system (1.1) reduces to the well-known Timoshenko system where the longitudinal displacement 𝒘 is not considered (𝒍 = 0), on the other hand, the energy associated with this system (1.1) remains constant when the time 𝒕 evolves, because it is an undamped system. That's why, different types of dampings should be added to the equations or at the limit, in order to stabilize this system that has been studied by many authors (see [14,3,4,17]).…”

Well-Posedness and Exponential Stability of the Von Kármán Beam With Infinite Memory

“…This nonlinear elastic systems incorporating wave equations govern the propagation of waves, oscillations, and vibrations of membranes, plates, and shells. The entire Von kármán's model in contrast to other fundamental models like the Euler-Bernoulli, Raleigh, or Timoshenko is appropriate for considering both transverse and longitudinal displacements for vibrating slender bodies with large deflection (for more discussion see [5][6][7]).…”