Michele Brun, mbrun@unica.it
Co-authors: Daniel Colquitt, Massimiliano Gei, Alexander B. Movchan, Natasha V. Movchan, Ian S. Jones
Transformation cloaking for flexural waves in elastic plates
Cloaking transformation for flexural waves in plates are considered. For the Kirchhoff-Love problem governed
by a fourth-order partial differential equation it is shown that the equation governing the problem is not invariant
with respect to cloaking transformation as opposed to the Helmholtz operator. The transformed equation finds
a consistent physical interpretation as a inhomogeneous orthotropic flexural plates in the presence of pre-stress
and in-plane external forces. Additionally, an asymptotic derivation from three-dimensional continuum elasticity provides a rigorous link between the model in question and elastic wave propagation in thin solids, showing
connection with non-symmetric formulation in vector elasticity studied in earlier works. Example on a regularized push-out transformation show the broadband cloaking effect within the plate Kirchhoff-Love plate theory.
The proposed physical interpretation of the transformed equation may lead to a refinement of the experimental
implementations.