Coherent wave reflection in integrable or chaotic symmetrical acoustical billiards

Abstract

This study is concerned with the distribution of flexural vibrations in plates excited with a Gaussian white noise. The distribution of energy can be characterized by its homogeneity and isotropy. Some particular geometries like the Bunimovitch stadium generate a field that is both homogeneous and isotropic. But other geometries produce a field that is homogeneous but not isotropic (like the rectangle panel) or non-isotropic and not homogeneous (like the circular panel). It is known that these features drive the establishment of diffuse field. However, in the present work, we show that even at high frequency and for these three particular geometries, the diffuse field cannot be reached rigorously. Owing to symmetries, the vibrational response is always enhanced on some particular lines and points by the effect of coherence between rays. The enhancement factors are predicted theoretically with the image-source method. The presence of energy enhancement is also shown experimentally by measuring the vibrational energy density in the 20 Hz–4 kHz frequency range for these three plates excited with a random white noise. Measurement of enhancement factors shows a good agreement with their theoretical predictions.