Ray chaos in an architectural acoustic semi-stadium system.

The semi-stadium system is composed of a semicircular cap and a rectilinear platform. In this study, a dynamic model of the side, position, and angle variables is applied to investigate the acoustic ray chaos of the architectural semi-stadium system. The Lyapunov exponent is calculated in order to quantitatively describe ray instability. The model can be reduced to the semi-circular and rectilinear platform systems when the rectilinear length is sufficiently small and large. The quasi-rectilinear platform and the semicircular systems both produce regular trajectories with the maximal Lyapunov exponent approaching zero. Ray localizations, such as flutter-echo and sound focusing, are found in these two systems. However, the semi-stadium system produces chaotic ray behaviors with positive Lyapunov exponents and reduces ray localizations. Furthermore, as the rectilinear length increases, the scaling laws of the Lyapunov exponent of the semi-stadium system are revealed and compared with those of the stadium system. The results suggest the potential application of the proposed model to simulate chaotic dynamics of acoustic ray in architectural enclosed systems.