Periodic orbit analysis of an elastodynamic resonator using shape deformation

Abstract

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.