  The dynamics of a (nonlinear) Berger plate in the absence of rotational
inertia are considered with inhomogenous 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 non- linear 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 [22]). 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 [24].
  We provide a parallel commentary (from a mathematical point of view) to the
discussion of modeling with Berger versus von Karman nonlinearities: to wit, we
describe the derivation of each nonlinear dynamics and a discussion of the
validity of the Berger approximation. We believe this discussion to be of broad
value across engineering and applied mathematics communities.
