Analytical Evaluation of the Acoustic Behavior of Multilayer Walls When Subjected to Three-Dimensional and Moving 2.5-Dimensional Loads

Abstract

This paper focuses on the analytical evaluation of the acoustic behavior of multilayer walls when subjected to 3D and moving 2.5D loads. The computations are performed in the frequency domain for a wall system composed of multiple solid and fluid layers. The pressure generated by the 3D load is computed as Bessel integrals, following the transformations proposed by Sommerfeld. The integrals are discretized by assuming the existence of a set of virtual loads equally spaced in a direction perpendicular to the plane of the wall. The expressions presented here allow the pressure field to be computed without discretizing the interfaces between layers. The full interaction between the fluid (air) and the solid layers is taken into account. As the 3D pressure field can also be computed as a summation of spatially sinusoidal harmonic line loads, which can be seen as a moving 2.5D load, this paper studies the contribution made to the global 3D response by the insulation provided by the wall when subjected to each of these loads. To illustrate the main findings, simulated responses are computed in the frequency domains for single and double walls that are subjected to 3D and moving 2.5D loads. Additionally, time responses have been synthesized using inverse Fourier transformations.