A Semi-Random Finite Element Modal approach for Turbulent Boundary Layer induced Sound Transmission


  • Ulf Tengzelius

Publish date: 2010-12-15

Report number: FOI-R--3027--SE

Pages: 27

Written in: English


  • FEM
  • stationary random
  • turbulent boundary layer
  • sound transmission
  • Monte Carlo Method
  • sampling
  • random response
  • dynamic response
  • frequency response
  • FRF


A method called 'Semi Random Finite Element Method' (SR-FEM) have been developed by FOI. The aim with the SR-FEM has been to extend the capability of classical finite element approaches for responses from stationary random excitations. The following report describe this method , which is summarized in a conference paper, AIAA 2010-3952, given at the "16th AIAA/CEAS Aeroacoustics Conference", Stockholm 7-9th of June 2010. Finite element (FE) based methods have previously been found quite limited concerning upper model size for computation of structural response and sound transmission from stationary random loads, such as from a turbulent boundary layer. It is well known that when solving a dynamic response problem for deterministic loads, introducing a modal base, the eigenvalue solution is by far the most CPU-time consuming part of the solution process. For a stationary random excitation though, in contrary, the matrix multiplications, following upon the modal base establishment, becomes significantly more costly than the eigenvalue solution. This is when applying a classic modal-FE approach. With the presented SR-FEM instead the CPU-time for this complete set of matrix multiplications tends to be of the same order as the CPU-time for the eigenvalue solution. With this follows that the upper limit in model size could be moved considerably upwards. This enables response studies for example of complete aircraft cabin sections in the frequency range of some kHz, which corresponds to the needs for a typical turbulent boundary layer excitation. SR-FEM is based on a random sampling among elements within the system matrices established for the computation of structural- or sound transmission response, and is general in the sense that any distributed stationary random load might be applied. The method limits the frequency resolution in relation to a classic FE-solution. In order to achieve a significant CPU-time gain, and at the same time a "sufficient" accuracy, one should typically stay to third octave band representations of the response. In other words, a frequency resolution which can be considered as sufficient in most applications. Since SR-FEM is based on fundamental laws of statistics, means for error estimates is automatically at hand. These error estimates might be used when applying termination criteria for computations. The examples given show an accuracy of around 1 dB per 1/3-octave band compared with a full "classic" modal/FE-approach.