Qualitative results on the dynamics of a Berger plate with nonlinear boundary damping


GÜVEN GEREDELİ P. , Webster J. T.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, cilt.31, ss.227-256, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.nonrwa.2016.02.002
  • Dergi Adı: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
  • Sayfa Sayıları: ss.227-256

Özet

The dynamics of a (nonlinear) Berger plate in the absence of rotational inertia are considered with inhomogeneous boundary conditions. In our analysis, we consider boundary damping in two scenarios: (i) free plate boundary conditions, or (ii) hinged-type boundary conditions. In either situation, the nonlinearity gives rise to complicating boundary terms. In the case of free boundary conditions we show that well-posedness of finite-energy solutions can be obtained via highly nonlinear boundary dissipation. Additionally, we show the existence of a compact global attractor for the dynamics in the presence of hinged-type boundary dissipation (assuming a geometric condition on the entire boundary (Lagnese, 1989)). To obtain the existence of the attractor we explicitly construct the absorbing set for the dynamics by employing energy methods that: (i) exploit the structure of the Berger nonlinearity, and (ii) utilize sharp trace results for the Euler-Bernoulli plate in Lasiecka and Triggiani (1993).