  We report the first definitive experimental observation of periodic orbits
(POs) in the spectral properties of an elastodynamic system. The Fourier
transform of the density of flexural modes show peaks that correspond to stable
and unstable POs of a clover shaped quartz plate. We change the shape of the
plate and find that the peaks corresponding to the POs that hit only the
unperturbed sides are unchanged proving the correspondence. However, an exact
match to the length of the main POs could be made only after a small rescaling
of the experimental results. Statistical analysis of the level dynamics also
shows the effect of the stable POs.
