Mathematical Simulation of Sound Propagation in a Building

The relevance of this work is determined by inadequacy of engineering methods for calculating sound insulation, which do not consider energy losses, dimensions of constructions, influence of adjacent elements, and structural sound transmission, which is particularly relevant in using lightweight and multi-layer enclosures. The lack of tools for direct calculation of sound and vibration levels makes it difficult to assess the compliance of projects with sanitary standards. Purpose: The aim of this work is to develop bases for mathematical simulation of the sound propagation in buildings in order to create engineering methods and software for calculating the sound insulation of enclosing structures, sound pressure levels in rooms, and vibration parameters with regard to direct, indirect, and structural energy transmission. Methodology: Energy methods (sound energy balance) and wave theory (sound energy transmission). Analytical models are used to calculate the sound insulation of single- and multi-layer structures, models of sound propagation in complex building fragments in accordance to GOST R EN 12354-1–2012 and the statistical energy analysis. Research findings: Mathematical models and algorithms are developed for a three-level calculation system: inherent sound insulation capacity of structures, sound insulation with indirect and structural transmission, sound and vibration levels in rooms based on statistical energy analysis. The proposed models form the basis for the creation of parametric software to design sound insulation in buildings, taking into account structural sound transmission.