Skip to main content
    • Aa
    • Aa
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 136, Issue 2
  • April 2006, pp. 385-413

Uniform boundary stabilization of the dynamical von Kármán and Timoshenko equations for plates

  • G. P. Menzala (a1) and A. F. Pazoto (a2)
  • DOI:
  • Published online: 12 July 2007

The full nonlinear dynamic von Kárm´n system depending on a small parameter ε > 0 is considered. We study the asymptotic behaviour of the total energy associated with the model for large t and ε → 0. Introducing appropriate boundary feedback, we show that the total energy of a solution of the corresponding damped model decays exponentially as t → +∞, uniformly with respect to the parameter ε > 0. As ε → 0, we obtain a damped plate model for which the energy also tends to zero exponentially. The limit system can be viewed as new variant of the so-called Timoshenko model. It consists of a second-order hyperbolic equation for transversal vibrations of the plate coupled with a first-order ordinary differential equation whose solution appears as coefficient of the plate model and takes into account (when ε → 0) the contribution of the tangential components.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *