Numerical and experimental investigation of the effect of structural links on the sound transmission of a lightweight double panel structure

Abstract

This paper examines various models predicting the influence of periodically spaced structural links on sound transmission through lightweight double panel structures. A baseline configuration made up from two aluminum plates connected through aluminum C-section channels and a fiberglass filled cavity has been specifically built and its TL measured for comparison and validation of the investigated models. First, classical decoupled approaches are outlined and adapted for the studied case. Next, a periodic model based on existing formulations is presented. The model allows for a 3D incident field and accounts for the absorption in the cavity with the help of an equivalent fluid model for the fiberglass. Three cases of coupling conditions are considered for the links: a mass–spring–mass approximation, a beam-type approximation and a beam-type approximation where the rigidity and the inertia of the beams are neglected. The measurements show that the bridged configuration strongly reduces the TL at mid and high frequency and exhibits pass/stop bands characteristic of periodic structures. The predictions of decoupled approaches capture the physics of the problem only approximately and with the integration of the mass of the connectors in the context of thin lightweight panels, their agreement with experimental data is further reduced. On the other hand, the results obtained with the periodic model are excellent over most of the studied frequency range. However, in the vicinity of the critical frequency of the thicker panel (around 6 kHz), an overestimation of the TL is observed. This suggests that the model will have to account better for damping and resonant transmission.

Introduction

Double panel structures filled with air or absorbent fiberglass can be found in a wide range of applications and were therefore extensively studied in the literature. A recent article by Hongisto [1] provided a detailed comparison of the prevalent models for the prediction of sound transmission through such constructions. Over the 20 models presented, only a few were able to deal with connections between the panels: Sharp [2], [3], Gu and Wang [4], Fahy [5] and Davy [6], [7]. In these four models, the problem was addressed by decoupling the total transmission in terms of a fluid-borne path through the cavity and a structure-borne path through the connectors. They will be referred here as “decoupled approaches”.

Yet, many other types of formulations were developed to include the effect of structural links. Among them, approaches taking advantage of the periodicity of the structure were presented by several authors. In the latter, the equations of motion of the plates include the reactions of the connectors in addition to the pressures due to fluid loading. To solve the associated systems, two methods are classically used. The first method was introduced by Mead and Pujara [8], [9] and consists of representing the response of the structure in terms of a series of space-harmonics. The principle of virtual work is then applied on one period of the system to solve its dynamics. Lee and Kim [10] employed this technique to study the radiation of a single stiffened plate subjected to a plane wave excitation. Wang et al. [11] extended the approach to double-leaf partitions connected through vertical resilient studs. Urusovskii [12] had previously studied the problem using space-harmonic series to represent the plates’ response, but he assumed rigid studs and did not use the principle of virtual work to formulate the dynamics. Instead, he introduced the “phase factor” associated with the force exerted on the plates by the stud as a result of oblique incidence in the equations of motion. The second method makes use of Fourier transform techniques. This is the case of Lin and Garrelick [13] who calculated sound transmission through double-plate structures attached periodically by rigid connectors. To study radiation under mechanical excitation forces of point connected, point connected with rib stiffening and rib connected structures, Takahashi [14] used the Fourier transform as well, but his equations did not include fluid loading. Ultimately, even if the solving procedure behind the two approaches is not similar, both lead to solutions in which the response is given as a series of space harmonics [15].

When simulations or experimental validations were conducted in the above-mentioned references, attention was principally focused on building constructions which are typically composed of plasterboard panels connected with wooden studs or metallic channels. Although they are not strictly equivalent to these structures, lightweight aircraft sidewall panels are good examples of double panel partitions since they are frequently made of periodically rib-connected panels with fiberglass in-between. Moreover, the rivets attaching the ribs to the plates and/or the trim mounts are close-spaced to provide stiffness. In comparison, the distance between the screws or nails used to bond the plasterboard panels to the wooden/metallic skeleton in buildings is normally larger. Craik and Smith [16] discussed the fact that when this spacing is small, the connection can be modeled by a continuous line. However, when it gets larger, each point can be assumed independent and so the coupling may be modeled as a series of independent point connections. The appropriate transition frequency between these two regimes occurs when a half bending wave-length on the plate fits between the nails or the screws. Considering the above-mentioned differences, using experimental or simulations results of building partitions may not be adequate to validate the performance of classical prediction models for lightweight double wall systems with periodic connections. The aim of this paper is therefore to examine experimentally and numerically the effect of periodically spaced mechanical links on the transmission loss of a double panel structure that is more representative of aircraft applications.

First, the studied structure is described (geometry, dimensions, connection details, etc.). Next, the decoupled approaches [2], [3], [4], [5], [6], [7] presented in Ref. [1] are outlined and adapted to the studied case. Afterwards, a periodic model integrating important features of previous models [8], [9], [10], [11], [12], [13], [14] is exploited and extended to account for the nature of the studied mechanical link and cavity absorption. This is done by using an equivalent fluid model for the fibrous material [17]. A result section in which the studied models are compared to measurements is finally presented. It is followed by a general discussion on the accuracy of the various prediction methods.