The mid‐frequency range finite element (MFR‐FE) method: MATLAB implementation and results

The mid‐frequency range finite element (MFR‐FE) method was developed by Christian Soize in the early 1980s, and it is well described in Soize’s book with Roger Ohayon [Structural Acoustics and Vibration, (Academic, New York, 1998), Chap. 7]. The method combines finite element equations and the frequency translation property of the Fourier transform to solve acoustics and vibration problems in the mid‐frequency range, at frequencies higher than possible with conventional finite element codes. In an effort to understand the method fully, an implementation of MFR‐FE was developed in MATLAB [Mathworks Inc., Natick, MA], a natural environment for prototyping algorithms involving matrices and signal processing. The FE formulation was built upon one already prepared by Kwon and Bang [The Finite Element Method Using MATLAB, (CRC, Boco Raton, FL, 1997)], and initial results were recently described [Paper AIAA–99‐1855, 5th AIAA/CEAS Aeroacoustics Conference]. The present talk will provide an overview of MFR‐FEs and give example results, extending those previously shown. One advantage of the method is that it can be used with other improvements in FE technology, such as hp adaptive formulations. [Work sponsored by NASA Langley Research Center Structural Acoustics Branch.]