Eigenfrequency spacing analysis and eigenmode breakdown for semi-stadium-type 2-D fields
Eigenfrequency spacing analysis and eigenmode breakdown for semi-stadium-type 2-D fields
复制标题
半体育场型二维场的特征频率间隔分析和特征模式击穿
DOI：
10.1016/s0022-460x(02)01640-1
复制
发表时间：
2003
影响因子：
4.7
通讯作者：
M. Tohyama
中科院分区：
文献类型：
--
作者：
Yoh;M. Tohyama
本文介绍了本征频率统计，包括模态模式和自由度的半体育场型2-D字段。作者数值研究了由2-D半体育场型边界包围的声场，作为隐藏混沌特性的边界的例子，以了解复杂声场的特性，并获得对声场设计的新见解。半体育场边界的一个极限是矩形边界，给出了一个规则的领域，而另一个极限是体育场边界，其中出现的混沌属性。数值结果表明，在所有情况下的本征频率间距可以表示为一族推广到非整数自由度的Γ分布。这种分形自由度可以解释为声场的自由度。对于常规极限情况，即，矩形情况下，分布是具有单位自由度的指数分布，而在混沌情况下，即，在体育场的情况下，它是自由度为2的维格纳分布。然而，作者分析了半体育场声场。本征频率分布函数的波动分析表明，偏度随着边界接近体育场条件而减小。模态模式也清楚地表明，在矩形的情况下，节点线的规则模式的中断，因为边界从矩形变形到体育场条件。通过声压分布偏度的减小也可以确认模态模式的突变。
This paper describes eigenfrequency statistics including modal patterns and degrees of freedom for a semi-stadium-type 2-D field. The authors numerically investigated sound fields surrounded by 2-D semi-stadium-type boundaries as examples of boundaries where chaotic properties are hidden, in order to understand the characteristics of complex sound fields and to gain new insight into sound-field design. One limit of the semi-stadium boundaries is a rectangular boundary that gives a regular field, while another limit is a stadium boundary in which the chaotic property emerges. The numerical results show that eigenfrequency spacing in all the cases can be expressed as a family of Γ distributions extended to a non-integer degree of freedom. This fractal degree of freedom can be interpreted as the degree of freedom of the sound field. For the regular limit case, i.e., a rectangular case, the distribution is the exponential distribution with the freedom of unity, while in the chaotic case, i.e., the stadium case, it is the Wigner distribution with a degree of freedom of two. The authors, however, analyze the semi-stadium sound fields. The analysis of the fluctuations in the distribution function for the eigenfrequencies showed that the skewness decreases as the boundary approaches the stadium condition. Modal patterns also clearly showed breaks of the regular pattern of nodal lines in a rectangular case as the boundary was deformed from the rectangular to the stadium condition. The breaks of the modal pattern could be also confirmed by decreasing of the skewness for the sound pressure distribution.