Department of Architecture, Xiamen University Tan Kah Kee College, Zhangzhou, Fujian 363105, China.
Chaos. 2013 Mar;23(1):013107. doi: 10.1063/1.4772969.
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.
半体育场系统由半圆形罩和直线形平台组成。在这项研究中，应用了侧位和角度变量的动力学模型来研究建筑半体育场系统的声射线混沌。通过计算 Lyapunov 指数来定量描述射线不稳定性。当直线形长度足够小时和大时，模型可以简化为半圆形和直线形平台系统。准直线形平台和半圆形系统都产生具有最大 Lyapunov 指数趋近于零的规则轨迹。在这两个系统中都发现了声射线局部化现象，如颤振回波和声音聚焦。然而，半体育场系统产生具有正 Lyapunov 指数的混沌声射线行为，并减少了声射线局部化。此外，随着直线形长度的增加，揭示了半体育场系统的 Lyapunov 指数的标度律，并与体育场系统的标度律进行了比较。结果表明，所提出的模型可用于模拟建筑封闭系统中声射线的混沌动力学。
