Синхронизация колебаний двух связанных пластин Бергера с нелинейным внутренним и граничным демпфированием. Часть 1

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 γ describing the intensity of plate coupling. We prove that the upper limit of the attractor for γ → ∞ belongs to the diagonal of the system phase space, which means that the coupled plates tend to synchronize (i.e. oscillate identically) as time and the coupling intensity tend to the infinity.