  We consider a thin and narrow rectangular plate where the two short edges are
hinged whereas the two long edges are free. This plate aims to represent the
deck of a bridge, either a footbridge or a suspension bridge. We study a
nonlocal evolution equation modeling the deformation of the plate and we prove
existence, uniqueness and asymptotic behavior for the solutions for all initial
data in suitable functional spaces. Then we prove results on the
stability/instability of simple modes motivated by a phenomenon which is
visible in actual bridges and we complement these theorems with some numerical
experiments.
