Scarring in vibrational modes of thin metal plates

Abstract

We report the first direct experimental observation of scarring phenomenon in transverse vibrational modes of a thin metal plate. The plate has the shape of a full stadium and clamped boundary conditions. Normal modes are imaged using time-averaged holographic interferometry, and modes corresponding to ``bouncing ball'' and higher order periodic trajectories are found. An eikonal approximation of the solution along classical trajectories of the stadium including nontrivial phase shifts at clamped boundaries yields a useful quantization condition for the observed modes.