Deviations from Poisson statistics in the spectra of free rectangular thin plates

TL;DR

This study reveals that the bending spectra of free rectangular thin plates exhibit deviations from Poisson statistics due to mode interactions, with results supported by numerical simulations and experimental measurements.

Contribution

It demonstrates the presence of wave chaos in the spectra of free rectangular plates and links spectral statistics to the Rosenzweig-Porter model, supported by experiments.

Findings

Frequency levels cross between different symmetry classes.

Within the same symmetry class, only avoided crossings occur.

Level spacing ratios deviate from Poisson distribution and match the Rosenzweig-Porter model.

Abstract

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distributions of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distribution disagrees with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. The expected Poissonian distribution is recovered for the simply supported rectangular plate.