Синхронизация колебаний двух связанных пластин Бергера с нелинейным внутренним и граничным демпфированием. Часть 2

Abstract

A system of Berger PDE's describing nonlinear oscillations of two identical elastically coupled plates with partially clamped and partially free boundary and nonlinear dissipation acting inside plate domain as well as on the free part of the boundary is considered. We are interested in the dependence of the structure of the system global attractor on the value of the parameter у describing the intensity of plate coupling. In this part of our research we describe the structure of the upper limit of the attractor for ϒ → ∞. We prove that it coincides with the set diag (21 x 21), which is the diagonal of the product of two samples of the attractor for a single plate equation. Moreover, under additional assumptions on the damping functions the attractor for the system of two coupled plates coincides with the set diag (21 x 21) for ϒ sufficiently large.