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

Area of Science:

• * Physics
• * Acoustics
• * Mechanical Engineering

Background:

• * Wave chaos is a phenomenon typically studied in quantum systems.
• * Rectangular plates exhibit complex vibrational behaviors influenced by geometry and boundary conditions.
• * Understanding spectral properties is crucial for predicting plate dynamics.

Purpose of the Study:

• * To investigate the emergence of wave chaos in the bending spectrum of free rectangular thin plates.
• * To analyze frequency level crossings and avoided crossings within different symmetry classes.
• * To compare experimental and numerical findings with theoretical models.

Main Methods:

• * Extensive numerical simulations varying plate aspect ratios.
• * Calculation of consecutive level spacing distributions for different symmetry classes.
• * Experimental measurement of normal-mode vibration amplitudes on aluminum plates.
• * Comparison with Poisson, Gaussian orthogonal ensemble, and Rosenzweig-Porter models.

Main Results:

• * Frequency levels from different symmetry classes were observed to cross.
• * Levels within the same symmetry sector exhibited only avoided crossings.
• * Level spacing distributions deviated from the Poissonian prediction.
• * Experimental vibration modes closely matched numerical predictions.
• * The Rosenzweig-Porter model accurately predicted the observed level spacing distributions.

Conclusions:

• * Wave chaos is demonstrable in the vibrational spectra of free rectangular plates.
• * The Rosenzweig-Porter model provides a suitable framework for describing these spectral properties.
• * Experimental validation confirms the accuracy of numerical simulations for plate vibrations.