# Airborne sound insulation of single and double plate constructions

Abstract: The sound insulation demands for dwellings and public building has increased over the years as the number of sound sources has grown. From the outside our homes are exposed to noise from cars, trains, airplanes, etc. Noise intrudes from our neighbours and their television and stereo equipments. Also noise from spaces for mechanical services systems tends to become more important due to increasing energy saving demands.This thesis presents new analytical models for predicting the sound reduction index of single or double plate systems. In the single plate case, a theoretical and experimental analysis of the air-borne sound transmission through a single plate is presented. The plate is assumed to be excited by a diffuse sound field and the velocity distribution of the plate is derived from the Kirchoff plate equation in the frequency domain. The resulting Fourier transform is evaluated using residue calculus and the solution is verified numerically. The analytical model is valid for a wide frequency range, both below, above and at the critical frequency. Special interest is paid to the area dependency of the sound reduction index.This technique is further expanded for the double plate case by adding another plate and an intermediate layer which is modelled as a locally reacting spring. The model is valid and continuous through both the mass-spring-mass resonance and the coincidence region. The results from the analytical models show good agreement with measured results in both the single and double plate case.A simplified model is also presented for the sound reduction index of finite size floating floors. The model is valid for two elastic plates with a resilient layer in between where the bottom plate, the load-bearing slab, is assumed to be excited with a diffuse airborne sound field. The top plate and the resilient layer compose the floating floor. The problem is solved for frequencies below, between and above the critical frequencies of the plates. Above the critical frequency of the load-bearing plate, but below that of the floating slab, the main coupling between the plates will occur at the coincidence angle of the load-bearing plate. Above the critical frequency of both plates, the main transmission will occur at the angle of coincidence of each plate. As the plates will interact, the sound insulation improvement will to some extent depend on the properties of the load-bearing slab. It is shown how the sound reduction index depends on the physical parameters and the geometry of the plates.