We consider the family of singularly nonautonomous plate equation with
structural damping utt+a(t,x)ut+(−Δ)ut+(−Δ)2u+λu=f(u), in a bounded domain Ω⊂Rn, with Navier
boundary conditions. When the nonlinearity f is dissipative we show that this
problem is globally well posed in H02(Ω)×L2(Ω) and has a
family of pullback attractors which is upper-semicontinuous under small
perturbations of the damping a