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  • 1
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    A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts (1976)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.
    Keywords: ACOUSTICS
    Type: NASA-TN-D-8186 , L-10607
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 2
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    A statistical theory of sound radiation from a two-dimensional lined duct (1979)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: A statistical theory coupled with a finite element theory is employed for investigation of sound radiation from a two-dimensional lined duct. The analysis does not utilize duct modes, and can be applied to a non-uniform duct with variable wall liner properties. Numerical results are presented for various shapes of the incident wave. The results are in good agreement with the Wiener-Hopf calculation for cases where the latter can be made.
    Keywords: ACOUSTICS
    Type: AIAA PAPER 79-1521 , American Institute of Aeronautics and Astronautics, Fluid and Plasma Dynamics Conference; Jul 23, 1979 - Jul 25, 1979; Williamsburg, VA
    Format: text
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    NASA TECHNICAL REPORTS
  • 3
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    A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner (1977)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.
    Keywords: ACOUSTICS
    Type: NASA-TM-74080 , Aeroacoust. Conf.; Oct 03, 1977 - Oct 05, 1977; Atlanta
    Format: application/pdf
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    NASA TECHNICAL REPORTS
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