Abstract: | A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic
plate, clamped at its boundaries, is excited by a turbulent boundary layer.
Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid,
baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid
in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with
a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this
boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains.
Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very
complex and unresolved task. Ducan and Sirkis 1] proposed a model for the two-way interactions between a membrane and a turbulent
flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified
by the displacement of the membrane. Howe 2] proposed a model for the turbulent wall pressure fluctuations power spectrum
over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between
the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the
plate, but the vibration of the plate does not modify the characteristics of the flow.
A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity
has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we
focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical
methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity;
(b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element
method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior
acoustic pressure.
A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos
model 3] and the Chase model 4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure.
In 3], this difference is explained by calculating a wavenumber transfer function of the plate. In 6], coupled beam-cavity
modes for similar geometry are calculated by the finite difference method.
This revised version was published online in July 2006 with corrections to the Cover Date. |