On the modeling of the diffuse field sound transmission loss of finite thickness apertures

Abstract

The modeling of the diffuse field sound transmission loss (TL) of apertures has been rarely considered in the literature. The aims of this paper are (i) to give a comprehensive review of the existing models, (ii) to propose a general efficient and rigorous numerical method to predict the diffuse field TL of apertures of rectangular and circular cross section, (iii) to provide the reader with numerical results regarding this indicator together with its relation with the normal incidence case for various geometrical configurations, and (iv) to conclude on the relevance of using such a sophisticated model compared to more classical normal incidence ones. The proposed approach is based on the description of the sound field inside the aperture in terms of propagating and evanescent acoustic modes. The radiation of the aperture is accounted for using a modal radiation impedance matrix. The coupled problem is solved in terms of modal contribution factors. The convergence of the approach is then investigated and the model is validated by comparisons with existing models for various configurations and excitations. Several numerical examples are provided regarding the normal incidence and diffuse field TL for various apertures and the relationship between these two indicators is discussed.

Prediction of the spatial characteristics of higher mode sound transmission through a periodic slit screen

“…Sgard, Nelisse and Atalia [9] presented a comprehensive review of the various approaches to modelling of sound transmission through finite thickness apertures. This review concluded that many of the existing models that consider the effect of higher-order modes in the aperture are too time consuming to implement.…”

“…Analysis was then presented for modelling diffuse field sound transmission that includes higher order contributions. In reference [9] it was noted that only including modes up the maximum frequency of interest was sufficient to capture the sound field. It was also noted that there was strong cross modal coupling between the (0,0) plane wave mode and higher order even-even modes and that for aspect ratios greater than one, the transmission models based only on plane waves may not be sufficient even at low frequencies, due to the low values for the cut-on frequency of the first higher order mode.…”

Noise propagation through open windows of finite depth into an enclosure.

“…In Figure 6, the insertion loss of the present system was compared to Sgard's result for windows of varying thickness and an obliquely incident plane wave. Recall, Sgard et al 8 modeled an aperture with half-space on each side. The plot in the upper right shows the insertion loss of an aperture versus frequency for aperture thicknesses of 1m, 0.5m, and 0.1m using Sgard's model.…”

“…Several approximations and numerical solutions have been proposed, [3][4][5] and an analytic solution has been developed by Pierce et al 6 for an aperture backed by an arbitrary acoustic system. Sauter and Soroka 7 developed a theoretical relationship for the transmission of sound between two reverberant rooms, and Sgard et al 8 developed a mathematical model for an aperture bounded on both sides by half-space. Experimental validation for this model was provided by Trompette et al 10 As shown in Figure 2, this model consisted of incident, reflected, and radiated waves existing in half-space coupled to aperture modes through the surface S 1 ; the aperture modes were then coupled to a wave radiating into a second half-space through S 2 .…”

Ultrasonic transmission through periodically perforated plates

“…However, a more rigorous and exact method relying in modal expansions has been derived in [97]. More recently [98,99] deal with diffuse field incidence and compare different methods theoretically and experimentally.…”