The finite layer method for modelling the sound transmission through double walls

Abstract

The finite layer method (FLM) is presented as a discretisation technique for the computation of noise transmission through double walls. It combines a finite element method (FEM) discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. It is used for solving the Helmholtz equation at the cavity inside the double wall, while the wall leaves are modelled with the thin plate equation and solved with modal analysis. Other approaches to this problem are described here (and adapted where needed) in order to compare them with the FLM. They range from impedance models of the double wall behaviour to different numerical methods for solving the Helmholtz equation in the cavity. For the examples simulated in this work (impact noise and airborne sound transmission), the former are less accurate than the latter at low frequencies. The main advantage of FLM over the other discretisation techniques is the possibility of extending it to multilayered structures without changing the interpolation functions and with an affordable computational cost. This potential is illustrated with a calculation of the noise transmission through a multilayered structure: a double wall partially filled with absorbing material.

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

“…Significant research has been carried out in the field of analytical and numerical prediction of noise behavior [7][8][9][10][11]. In most cases, simple plate-like structures were studied and analytical or semi-empirical formulas were derived [12].…”

Numerical estimation of coupling loss factors in building acoustics

“…Modal analysis [9] is used for solving the acoustic part of the problem. This technique exploits the simple geometry of the problem to achieve an accurate result with less computational cost than a finite element discretisation.…”

“…This technique exploits the simple geometry of the problem to achieve an accurate result with less computational cost than a finite element discretisation. However, for a more complex geometry the problem might be solved with other discretisation techniques, such as the finite layer method [9] or the finite element method [23].…”

“…An error propagation analysis is performed, identifying the best expressions to use in the CLF computation. At the end of the section, the deterministic approach [8,9] is briefly reviewed. In Section 3 some application examples are shown.…”

Application of Finite Layer Method in Pavement Structural Analysis

“…In the next several years, researchers applied the FLM in groundwater flow models [27] and analyses of 3D Biot consolidation of layered transversely isotropic soils [28]. Recently, the FLM was applied for modeling the noise transmission through double walls [29]. analytical model, called 3D-Move uses a continuum-based FLM to compute pavement responses [30,31].…”