Theoretical analysis of sound reduction property in one-dimensional random duct and its application to noise control

我们知道，波在随机介质中不能长距离传播，当场被激发时，波被限制在一个小区域内。在物理学中，它被称为“局域化”，这种现象与波在某一宽频带内的截止（不传播）状态密切相关。由于在随机介质或随机载荷中传播的声音沿距离会表现出强烈的指数衰减，因此可以利用这种特性作为消声器来降低声音噪声。另一方面，一维声管道可以用微波波导研究中常用的传输线模型来表示。在本研究中，我着重研究了一维管道（随机管道）的声衰减特性，并通过计算机仿真证明了所提出理论的有效性。我在2005年和2006年获得的结果如下。【2005年】：作为研究的第一步，我用传输线模型来表达风管中的声场，在此基础上对普通一维风管进行了理论分析，并进行了计算机模拟。在电路表示的基础上，从理论上提出了管道中存在随机介质时的消声特性。为了证实分析的有效性，我进行了计算机模拟，并证明了强指数衰减的存在。这些研究结果已在科学杂志上发表，并在国内会议上发表。[2006年]：继2005年对随机降噪问题的基本考虑之后，我从理论上提出了管道中存在随机载荷情况下的降噪特性，广泛的模拟表明，所提出的方法也使我们能够引起强指数衰减。这些结果已在国际会议上提出。

It is known that a wave cannot propagate long distance in random media and is confined in a small region when the field is excited. In physics it is called the "localization", the phenomenon which is closely related to the cut-off (non-propagating) state of waves in a certain broad frequency band. It is expected that this property can be utilized as a muffler to reduce the sound noise because the sound propagating in random media or random loadings would exhibit strong exponential decay along distance. On the other hand, a one-dimensional acoustic duct can be expressed by a transmission line model commonly used in the study of microwave waveguide. In this research, I focus on the sound decaying property of one-dimensional duct (random duct) and demonstrate the validity of the proposed theory through a computer simulation. The results I obtained in 2005 and 2006 are listed below.[2005 year] : As the first step of research, I expressed the sound field in duct by a transmission line model, on which I theoretically analyzed the ordinary one-dimensional duct and carried out computer simulation. Based on the circuit representation, I theoretically proposed the sound reduction property in a case when there exist random media in duct. To confirm the validity of the analysis, I performed the computer simulation and showed the existence of the strong exponential decay. These results have been published in a scientific journal and presented in domestic conference.[2006 year] : Following to the fundamental consideration on the sound reduction problem with randomness in 2005, I theoretically proposed the sound reduction property in a case when there exist random loadings in duct and the extensive simulation makes it clear that the proposed method also enables us to cause the strong exponential decay. These results have been presented in international conferences.