This dissertation proposes an analytical method that determines an optimal absorptive material arrangement (AMA) on an enclosure`s interior surface. The optimal AMA makes a quiet zone in enclosure, which has minimum acoustic potential energy density $ε_p$. The absorptive material arrangement on enclosure`s wall eventually alters boundary condition and results to change enclosure`s acoustic energy distribution.
It is a classical boundary value problem. However its solution is not available because of its rather complex boundary condition. The boundary condition is often called as mixed boundary condition. To see the relation between this mixed boundary condition and internal sound field, we need to develop certain method that can allow us to study the relation. This has to be a solution that can predict sound field of general three-dimensional space. As a starting point; this obviously leads us to ultimate three-dimensional analysis and more importantly provides physical insights associated with this problem, for example, how the arrangement really affects the interior sound field at what extent. We started with a two-dimensional square cross-sectioned enclosure. A dimensionless parameter study is performed to evaluate the effect of a periodic absorptive strip arrangement on the entire enclosure`s acoustic potential energy density. In this analysis, the acoustic potential energy density is evaluated as a function of a dimensionless ratio $\tildeΔ$ of an absorptive strip arrangement period to a wavelength. As a result a critical ratio $\tildeΔ^*$ (i.e. $\tildeΔ=1$ ), which characterizes the acoustic potential energy density variation due to an absorptive strip arrangement period change, is proposed. The results demonstrate that the acoustic potential energy density tends to decrease monotonously as reducing the ratio, provided that $\tildeΔ$ is smaller than $\tildeΔ^*$ ; its decreasing rate essentially diminishes to be negligible.
There have been a few researches [R. J. Bernhard and S. Takeo, “A finite element procedure for design of cavity acoustical treatment,” J. Acoust. Soc. Am. 83, 2224-2230 (1988); T. C. Yang, C. H. Tseng, and S. F. Ling, “A boundary-element-based optimization technique for design of enclosure acoustical treatments,” J. Acoust. Soc. Am. 98, 302-312 (1995); V. Martin and A. Bodrero, “An introduction to the control of sound field by optimizing impedance locations on the wall of an acoustic cavity,” J. Sound Vib. 204, 331-357 (1997).] that propose analytical procedures to optimize an enclosure`s acoustic treatment and show its application example. However, they did not consider the absorptive material`s availability and its statistical distribution. These are the key factors for the practical materialization of the designed optimal AMA. Whatever the performance of the designed optimal AMA is good, it is useless if the required impedance, i.e. the optimal absorptive material is not available. In this context, the proposed method assumes that the available absorptive materials` admittances and its statistical distributions are prescribed. These absorptive materials` admittances are used as a search space for the optimization so that an optimal AMA from it can be materialized. The absorptive materials` statistical distributions are required to evaluate the change of the AMA system`s performance due to the possible variation of the absorptive materials` impedance. The possible variation means the impedance change in the predefined distribution.
Two analysis programs; a BEM simulation program and a genetic algorithm are required to study the relation between interior acoustic field characteristics and AMA distributions. The BEM simulation evaluates the $ε_p$ under the prescribed AMA; the genetic algorithm searches the optimal AMA by referring the $ε_p$ evaluated from the BEM simulation. In the BEM simulation, the absorptive material arrangement is expressed as a vector, which is denoted as an AMA vector. Besides, an admittance vector of which elements are admittances of available absorptive materials and an AMA matrix that transforms the admittance vector into the AMA vector are defined. The AMA matrix is also used as a chromosome in the genetic algorithm so that it functions to relate the BEM simulation to the genetic algorithm.
As an application example, the proposed method is applied to make a quiet zone in a car cabin. The results show that the quiet zone generation is possible with absorptive materials of which absorption coefficient is relatively low. The optimal AMA, compared to a completely rigid wall condition, reduces $ε_p$ of the quiet zone by 13.4 dB. In this case, the sound pressure level of the car cabin`s cross-section shows that the optimal AMA moves the nodal region of a mode that dominates the sound field to the quiet zone. The result, in case of low modal density sound field, suggests that moving the nodal region by using AMA yields a good control performance in a quiet zone generation.
