Energy Flux in Thin Plates

A formula for energy flux due to vibrations in a thin plate modelled by Kirchhoff theory is derived by considering a Mindlin plate and taking the low frequency (or low thickness) limit. It is shown that a term that is usually neglected in Kirchhoff theory persists close to free edges. This term does not affect the transverse displacement, but it does affect the energy flux. The new flux formula conserves energy and evaluates to zero along fixed, free and simply supported edges. An example problem, in which edge waves are excited by a point source located in a semi-infinite plate, is considered. Numerical calculations show that the energy radiated into the far field matches the energy introduced by the source.