Diffusion equation modeling for sound energy flow analysis in multi domain structures

Abstract

This study investigates reliable models and methods to be applied in sound field analysis of multi-domain structures. The case structures are two monuments, namely, Süleymaniye Mosque and Hagia Sophia in İstanbul. These are both multi-volume spaces with many smaller sub-volumes coupled to each other by coupling apertures in form of arches. A key concern of the study is to examine energy flow decays and understand the mechanism of multi-slope sound energy decays. The methodology involves diffusion equation model (DEM) application in a finite-element scheme for sound energy flow analysis. Energy flow decays, energy flow dips, and spatial flow vectors are examined for single versus multi-domain DEM solutions. It is concluded that specification of different domains with individual diffusion coefficients is a critical setting such that, if not assigned correctly, may mislead the results. The energy flow vector analysis has enabled us to comprehend the architectural features in relation to such energy flow decay dip occurrence. The computational efficiency of DEM is also discussed. The DEM application in this study has proved to be a powerful and practical method in room acoustics applications, specifically for multi-rate decay investigations.

Acoustical Impact of Architectonics and Material Features in the Lifespan of Two Monumental Sacred Structures

“…After field tests, the models were tuned and further utilized for experimentation of different materials of the original state and fully-occupied conditions. The DEM method was utilized for in depth-analysis and understanding of the probable reasons of multi-slope decay formation in such multi-domed monumental structures by energy flow vector, energy flow decay, and spatial sound energy distribution analysis and results are presented in previous papers [15,46,47].…”

Neural network for multi-exponential sound energy decay analysis

“…For example, the reverberation time can be determined by estimating the parameter T 1 for an EDF model with K = 1. Decay models of higher order have successfully been used to measure the absorption coefficients of materials 16 or characterize the sound decay of coupled spaces 17,18 .…”

“…By choosing the model with the maximum IBIC, the Bayesian framework balances the degree of fit and a potential overparameterization. The IBIC for the model of order K is given as 19 IBIC K = 2 ln( ˆ K ) − (2K + 1) ln(L) , (18) where ˆ K is the maximum-likelihood determined with the slice-sampling algorithm, and L is the number of EDF samples.…”

Effects of carbon nanomaterials and MXene addition on the performance of nitrogen doped MnO2 based supercapacitors

“…e l s e v i e r . c o m / l o c a t e / a p a c o u s t [25][26][27][28], statistical energy analysis [29][30][31][32], ray-based geometrical acoustics [33][34][35], diffusion equation model [36][37][38][39][40] and surface coupling approach [41]. On the other hand, there are comparisons of different numerical simulation approaches utilized in coupled space studies [42].…”