Fifth International Congress on Sound and Vibration

This paper analyzes the chaotic characteristics of irregular systems using both wave theory and ray theory. In ray theory, we visualize the chaotic properties of the ray propagation trajectories in a chaotic wave field. We found that the trajectory of the billiard problem with a stadium boundary condition has the same sensitivities to the initial conditions as does the mapping process on a logistic map does. In wave theory, we investigate the distribution statistics of the eigenvalues and the correlation dimension of the higher-eigenmodes in an irregular system by using the Finite Element Method (FEM). We clarify the relationship between the curvature of the stadium boundary and the statistical degrees of freedom of the wave field. The eigenvalue spacing statistics were estimated by 17distributions with fractional freedoms between 1 and 2.