Xiaojian Yu and Yu Zhang
Architectural acoustics, ray, semi-stadium, chaos, Lyapunov exponent, diffusion
In this paper, a dynamic model is applied to investigate acoustic ray diffuse behaviours of an architectural semi-stadium (SS) system. The semi-stadium system is composed of a semicircular cap and a rectilinear platform. A group of recursion formula are given to determine the motion of the acoustic ray. Lyapunov exponent analysis is applied to quantitatively describe ray diffuse behaviours. The semi-stadium system produces a chaotic ray with a positive Lyapunov exponent. Ray angle perturbation will be sufficiently amplified so that the rays that are initially adjacent diffuse uniformly across the room. Ray diffuse behaviour of the SS system illuminates ray localizations. Furthermore, the characteristic diffuse time effectively describes the time to reach the diffuse ray system. The dependence of the characteristic diffuse time on the rectilinear length is investigated. The characteristic diffuse time of the SS system sufficiently increases when the rectilinear length is sufficiently small or large. The results suggest the potential application of the dynamic model to describe diffuse behaviours of acoustic ray in architectural enclosed systems.
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