  We study asymptotic synchronization at the level of global attractors in a
class of coupled second order in time models which arises in dissipative wave
and elastic structure dynamics. Under some conditions we prove that this
synchronization arises in the infinite coupling intensity limit and show that
for identical subsystems this phenomenon appears for finite intensities. Our
argument involves a method based on "compensated" compactness and
quasi-stability estimates. As an application we consider the nonlinear
Kirchhoff, Karman and Berger plate models with different types of boundary
conditions. Our results can be also applied to the nonlinear wave equations in
an arbitrary dimension. We consider synchronization in sine-Gordon type models
which describes distributed Josephson junctions.
