  In this paper we formulate the problem of elastodynamic transformation
cloaking for Kirchhoff-Love plates and elastic plates with both the in-plane
and out-of-plane displacements. A cloaking transformation maps the
boundary-value problem of an isotropic and homogeneous elastic plate (virtual
problem) to that of an anisotropic and inhomogeneous elastic plate with a hole
surrounded by a cloak that is to be designed (physical problem). For
Kirchhoff-Love plates, the (out-of-plane) governing equations of the virtual
plate is transformed to those of the physical plate up to an unknown scalar
field. In doing so, one finds the initial stress and the initial tangential
body force for the physical plate, along with a set of constraints that we call
cloaking compatibility equations. These constraints involve the cloaking
transformation, the unknown scalar field, and the elastic constants of the
virtual plate. It is noted that the cloaking map needs to satisfy certain
conditions on the outer boundary of the cloak and the surface of the hole. In
particular, the cloaking map needs to fix the outer boundary of the cloak up to
the third order. Assuming a generic radial cloaking map, we show that cloaking
a circular hole in Kirchoff-Love plates is not possible; the cloaking
compatibility equations and the boundary conditions that the cloaking map needs
to satisfy are the obstruction to cloaking. Next, relaxing the pure bending
assumption, the transformation cloaking problem of an elastic plate in the
presence of in-plane and out-of-plane displacements is formulated. In this
case, there are two sets of governing equations that need to be simultaneously
transformed under the cloaking map. We show that cloaking a circular hole is
not possible for a general radial cloaking map; the cloaking compatibility
equations and the boundary conditions that the cloaking map needs to satisfy
obstruct cloaking.
