Experimental data Stadium from Coherent wave reflection in integrable or chaotic symmetrical acoustical billiards

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 which is both homogeneous and isotropic. But other geometries produce a field which is homogeneous but not isotropic (like the rectangle panel) or non-isotropic nor 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.

本研究聚焦于受高斯白噪声（Gaussian white noise）激励的薄板弯曲振动分布。能量分布可通过其均匀性与各向同性进行表征。部分特定几何结构，如布尼莫维奇体育场（Bunimovitch stadium），可生成同时具备均匀性与各向同性的振动场；而其他几何结构则会产生仅具备均匀性却不具备各向同性的振动场（如矩形板），或是既不具备各向同性也不具备均匀性的振动场（如圆形板）。已知上述特征会驱动漫射场（diffuse field）的形成。然而在本研究中，我们证明即便在高频条件下，针对上述三类特定几何结构，也无法严格实现漫射场。由于对称性的存在，光线间的相干效应会使得部分特定直线与点上的振动响应始终得到增强。我们通过镜像源法（image source method）从理论上预测了该增强因子。通过在20 Hz–4 kHz频率范围内对这三类受随机白噪声激励的薄板开展振动能量密度测量，实验也证实了能量增强现象的存在。增强因子的测量结果与理论预测值吻合良好。