  We consider the Cauchy problem for plate equations with rotational inertia
and frictional damping terms. We will derive asymptotic profiles of the
solution in L^2-sense as time goes to infinity in the case when the initial
data have high and low regularity, respectively. Especially, in the low
regularity case of the initial data one encounters the regularity-loss
structure of the solutions, and the analysis is more delicate. We employ the
so-called Fourier splitting method combined with the explicit expression of the
solutions (high frequency estimates) and the method due to Ikehata (low
frequency estimates).
