Study on Acoustic Field with Fractal Boundary Using Cellular Automata
In the present study, characteristics of the acoustic field in an enclosure bounded by fractal walls are investigated using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid. The dynamics of
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Abstract. In the present study, characteristics of the acoustic field in an enclosure bounded by fractal walls are investigated using Cellular Automata (CA). CA is a discrete system which consists of finite state variables arranged on uniform grid. The dynamics of CA is expressed by temporary updating the states of cells according to the local interaction rules, defined among a cell and its neighbors. In this paper, the effect of fractal shaped boundary structure to the reverberation and sound absorption characteristics of an enclosure is investigated for two dimensional acoustic wave propagation model described by CA. Local rules are provided for the construction of fractal patterns as well as representation of wave propagation phenomena. It is known by the numerical simulations that the damping enhancement and also frequencyselective absorbing behavior is seen for specific fractal patterns and stage numbers.
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Introduction
Among various kinds of sound dissipation schemes, the use of absorptive materials such as porous materials is the most common and significant technique which is widely used for room acoustics and various electric devices. However, the application of such dissipative materials may be limited by their weights, placement and costs. Basically, such absorbing materials can mitigate sound effectively at mid and high frequency range, whereas it is physically well known that they are not much effective for the low frequency regions. On the other hand, the sound may be reduced by appropriately arranging the acoustic boundary or the sound transmission paths where the sound waves are well diffracted and interfered with each other so that the reverberation characteristic is changed. Several works have been done regarding this issue, where the wave is dissipated depending on the irregularity of the perimeter [2]-[7]. It is also reported that certain acoustic modes are trapped within a part of such irregular boundary which contributes to enhance the damping effect. The fractal nature would be a measure for evaluating complexity of the boundary.The geometric definition of fractal structure, namely the fractal dimension was first proposed by Mandelbrot in 1975 [1], in order to describe the irregularity of object geometries. The self-similar patterns can be seen in many natural H. Umeo et al. (Eds): ACRI 2008, LNCS 5191, pp. 282–290, 2008. c Springer-Verlag Berlin Heidelberg 2008
Study on Acoustic Field with Fractal Boundary Using Cellular Automata
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systems such as in coastlines, clouds, snow flakes and even in economic trends, where the fragments having similar patterns to the whole structures. Typical applications of fractal geometry include artistic designs of computer graphic pictures, engineering applications as the way to analyze spatio-temporal characteristic of images and information. Their intrinsic physical properties are also of general interest and various kinds of researches have also been done with the expectations that any peculiar phenomena may appear due to its self-similarity. Among many physi
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