Analytical evaluation of the acoustic insulation provided by double infinite walls

Abstract

The acoustic insulation provided by infinite double panel walls, when subjected to spatially sinusoidal line pressure loads, is computed analytically. The methodology used extends earlier work by the authors on the definition of the acoustic insulation conferred by a single panel wall. It does not entail any simplification other than the assumption that the panels are of infinite extent. The full interaction between the fluid (air) and the solid layers is thus taken into account and the calculation does not involve limiting the thickness of any layer, as the Kirchhoff or Mindlin theories require. The problem is first formulated in the frequency domain. Time domain solutions are then obtained by means of inverse Fourier transforms using complex frequencies.The model is first used to compute the sound reduction provided by a double homogeneous brick wall, with identical panels, when illuminated by plane sound waves. The results are then compared with those provided by the simplified method proposed by London, which was later extended by Beranek (LondonBeranek method). The limitations of the simplified London-Beranek model, namely, its applicability only to double walls with identical mass, subjected to plane waves, and its failure to account for the coincidence effect, are overcome by the method proposed.Time signatures are produced to illustrate the different sound transmission mechanisms. Several types of body and guided waves are originated, giving rise to a complex dynamic system with multiple reflections within the solid and fluid layers and the global resonance of the system. The effect of the cavity absorption is considered by attributing a complex density to the air filling the space between the two wall panels. Absorption attenuates the dips of insulation controlled by the cavity resonances. Several simulations are then performed for different combinations of wall and air layer thickness to assess the influence of this variable on the final acoustic insulation. The influence of the air cavity on sound reduction was found to be dependent on the frequency. At low frequencies a better performance was achieved for thicker air layers, while at higher frequencies a thinner air layer is preferable. The use of wall panels with different mass resulted in the wall performing better, particularly for high frequencies. 0022-460X/03/$ -see front matter r

Prediction of airborne sound and impact sound insulation provided by single and multilayer systems using analytical expressions

“…In this work, a generalization of the technique proposed by Tadeu et al [11][12][13] is performed in order to handle multilayer systems and the application of impact loads. The referenced authors derived a procedure to calculate the pressure field generated by a single panel, based on knowing the solid layer displacement potentials and the pressure potentials due to excitation by a spatially varying harmonic line load.…”

“…The sum of airborne and impact sound insulation is computed for the single concrete layer and integrations in the 1/3 octave band frequency are performed. Responses provided by the analytical model, experimental results and expression (13) are plotted in Fig. 7c.…”

“…The formulation of a set of analytical solutions for calculating the acoustic insulation provided by single and double walls when submitted to incident pressure fields has been presented in earlier work [11][12][13]. This paper generalizes that model to solve structures with an arbitrary number of elastic and acoustic layers, also allowing the application of three-dimensional impact loads.…”

A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls

“…This is due to the geometrical criteria of transmission suites and standardized conditions of acoustic fields that lead to specific acoustic loading of the test specimen under fluid-structure interaction (FSI) [13]. Moreover, predicting the airborne sound transmission through multilayer structures with cavities and structural links, under the influence of FSI, is a rather difficult task due to the complex dynamic system involved [13][14][15][16][17].…”

Parametric Sensitivity Analysis of Factors Affecting Sound Transmission Loss of Multi-Layered Building Elements Using Taguchi Method

“…Influence of air-cavity on sound reduction has been found to be dependent on frequency. At low frequencies, a better performance is achieved for thicker layers; while at higher frequencies a thinner air-layer is preferable (António et al, 2003). Attachment via resilient channels and steel studs is instrumental in increasing sound transmission loss.…”