Finite element modeling for predicting sound insulation of fixed windows in a laboratory environment

This paper presents discussion of the prediction capability of three numerical models using finite element method for predicting the sound reduction index (SRI) of fixed windows having different dimensions in a laboratory environment. The three numerical models tested here only discretize the window part or windows part and the space around the windows to reduce the necessary computational cost for vibroacoustics simulations. An ideal diffused sound incidence condition is assumed for three models. Their predictability and numerical efficiency were examined over five fixed windows with different dimensions compared to measured SRIs. First, the accuracy of the simplest model in which the window part is only discretized with finite elements was examined. Acoustic radiation to the transmission field is computed using Rayleigh’s integral. Calculations were performed under two loss factor setups respectively using internal loss factors of each material and measured total loss factor of each window. The results were then compared with the measured values. Results revealed the effectiveness of using the measured total loss factor at frequencies around and above the coincidence frequencies. Subsequently, we tested the prediction accuracy of a numerical model that includes a niche existing in a laboratory environment. Also, hemispherical free fields around the window are discretized using fluid elements and infinite fluid elements. The results underscored the importance of including a niche in a numerical model used to predict sound reduction index below 1 kHz for smaller windows accurately. Nevertheless, this numerical model, including a niche, entails high computational costs. To enhance the prediction efficiency, we examined the applicability of a weak-coupling model that divides calculation procedures into three steps: (1) incidence field calculation to the window surface, (2) sound transmission calculation in fixed windows, and (3) sound radiation calculation from a window surface to a transmission field. Results revealed that the weak-coupling model produces almost identical results to those of a strong-coupling model, but with higher efficiency.

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