防音防振機構の確率評価に関する一般理論と一重壁への適用 : 防音防振機構の統計学的評価に関する方法論的基礎研究I

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Random city noise and vibration encountered in our living environment appear as a result of the diversified fluctuations of circumstances whose social causes are more complex than pure physical ones. From the practical viewpoint of control for such environmental noise and vibration pollution, statistics, such as the median, L_5 and L_<10>(in general, L_α sound or vibration level), are very important for evaluating of human response, these statistics directly combined with the probability distribution form of random noise and vibration, as well as the lower order statistics like average, variance and L_<eq>. Thus, it is very important to establish a systematic method for evaluating the effect of noise or vibration control systems on the widely-used standard index such as L_α. In this paper, a general study has been proposed in special reference to the unified evaluation procedure of noise or vibration control systems, when the general random noise or vibration wave, having arbitrary liner and nonlinear correlation and level probability distribution properties, is passed through the various types of liner noise or vibration control system. That is, by using only a case of a noise control system as an example, the multivariate Hermite series expansion expression, Eq. (1), can be universally employed for the statistical description of the incident sound pressure wave, x(t), with arbitrary correlation and distribution properties. The transmitted sound pressure wave, y(t), from the noise control system, is then given by Eq. (3), where A(Δ___={a_<ij>})denotes a (N×K) coefficient matrix reflecting the proper impulse response and frequency characteristics of the noise control system. The multivariate joint characteristic function, m_y(θ), with respect to the stochastic vector, y( col. {y_1, y_2, ・・・, y_N}, y_i=y(t_i)), has been derived as Eq. (12) and the corresponding multivariate joint probability density function as Eqs. (21) and (22). Thus, the effect of correlation and probability distribution properties of the incident sound wave and the individual characteristics of the noise control system on the probability distribution form of transmitted sound pressure wave are reflected in the expansion coefficient, D(m_1, m_2, ・・・, m_N) (cf. Eq. (14)) and the parameters, μ_y and σ^2_<pq> (cf. Eq. (11)). The important quantity directly connected to the evaluation of practical noise control problems is the noise intensity rather than the sound pressure itself. We have given our special attention again to the univariate characteristic function, Eq. (29), with respect to the noise intensity, E. By using the integral relations, Eqs. (30) and (32), two probability distribution expressions have been derived as Eq. (34) for the incident noise intensity and Eq. (35) for the transmitted noise intensity. The application of this statistical method was considered for a simple but basic noise control system such as a single-wall, whose frequency transfer function and discrete impulse response function are given by Eqs. (36) and (37), respectively. Experimental simulation was carried out in terms of two models of the normal-incident wave and a model of a homogeneous single-wall whose time constant was chosen within 1/20〜1/80(plate surface density, m=10. 4〜41. 4kg/m^2). The corresponding experimental results are shown in Figs. 1 (a)〜(d) and 2. Figures 3 and 4 give the noise reduction effect of a single-wall in terms of the difference between the incident and transmitted noise intensity level, L_α. Thereby, we were able to observe a good agreement between theory and experimentation. As is well-known, the random-incident mass law depends upon the additive property with respect to the average noise energy, so that it holds only when the average energy of transmitted noise wave is considered. When it is especially desired to make the evaluation in terms of the probability distribution for the transmitted noise intensity, we mu
社団法人日本音響学会の論文
1978-06-01

防音防振機構の確率評価に関する一般理論と一重壁への適用 : 防音防振機構の統計学的評価に関する方法論的基礎研究I

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