X. Yu and Y. Zhang (PR China)
Architectural acoustics, ray, semi-stadium, chaos, and Lyapunov exponent
In this study, a dynamical model is proposed to investigate the ray dynamics of an architectural acoustic semi-stadium system. The semi-stadium system is composed of a semicircular cap and a rectilinear platform. A group of recursion formula is derived to determine the motion of the ray trajectory. Lyapunov exponent analysis is applied to quantitatively describe the ray dynamics. The semi-circular system produces a periodic trajectory with Lyapunov exponent approaching zero and causes the sound focusing. However, the semi-stadium system produces a chaotic or aperiodic ray behaviour with positive Lyapunov exponent and reduces ray localizations. The results suggest the potential application of the proposed model to describe irregular dynamics of acoustic ray in architectural enclosed systems.
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