Modeling of Aircraft Structural-Acoustic Response to Complex Sources Using Coupled FEM/BEM Analyses

Abstract

A modeling process is developed for low-frequency, structural-acoustic response of aircraft structures due to random sources. The analysis is based on using the finite element method (FEM) to represent the structure, coupled to a boundary element method (BEM) representation of the interior and exterior acoustic domains. A random source module within the BEM analysis is used to incorporate the sources, which are defined in terms of the cross-spectra of the exterior fluctuating pressure field. The initial implementation is made in terms of a diffuse field, which has a relatively simple formulation and extensive data available for validation. The source definition is extended to include turbulent boundary layer (TBL) noise, due to its prevalence as a noise source throughout the passenger cabin. It is also extended to include engine shockcell noise, where the high coherence and lowfrequency content of the source makes it well-suited for a coupled FEM/BEM analysis. The general expression for the cross-spectra consists of three terms: the power spectrum, coherence, and a phase factor. The detailed form of these terms is determined such that it yields the best match with measurements of the source field. I. Introduction The following paper describes the process of integrating complex aero-acoustic sources into a hybrid Finite Element-Boundary Element Method (FEM-BEM) analysis for low-frequency predictions of cabin noise. The process is based on the definition of the diffuse field of a reverberant chamber and extended to represent turbulent boundary layer and engine shockcell noise sources. The noise source models are defined in terms of the cross spectra of the fluctuating pressure, which is applied as a distributed loading on the coupled, structural-acoustic model. A diffuse field is the starting point, due to its relatively simple formulation and the availability of extensive test data for validation. The analytic formulation of the diffuse field cross spectra is based on an infinite series representation of randomly distributed plane waves. 1 This plane wave representation presents two possible modeling methods to define an equivalent source field: 1) a distributed loading using the cross-spectra and 2) a truncated series of plane waves explicitly represented within the BEM model. The truncated series of plane waves method, along with laboratory transmission loss data, is used to initially validate the cross spectra approach. The predominance of turbulent boundary layer (TBL) noise in cabin acoustic measurements makes it essential that the prediction capabilities be extended beyond the diffuse field. The definition of the cross spectra for TBL is based on a semi-analytic formulation of the fluctuating pressure field measured in flight and wind-tunnel tests. The hybrid FEM-BEM analysis of the response due to TBL is compared against a similar implementation of the source as a mechanical loading in an uncoupled, structural FEM model. The uncoupled analysis method is then validated against flight test accelerometer data. Compared with the boundary layer, the shockcell source field is well-correlated and has strong low-frequency content. These attributes make it ideal for an FEM-BEM analysis and predicting shockcell noise is the ultimate goal of this modeling process. The initial approach involved using a numerical model of the source field to generate the full cross spectra, but this proved to be computationally inefficient. The approach currently being developed is to use shockcell noise measurements to define a semi-analytic representation based on the form of the TBL source.