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The Quarterly Journal of Mechanics and Applied Mathematics 1982 35(3):367-390; doi:10.1093/qjmam/35.3.367
© 1982 by Oxford University Press
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SOLUTION OF THE UNSTEADY SUBSONIC THIN AIRFOIL PROBLEM

MARC H. WILLIAMS

( Department of Aeronautics and Astronautics, Purdue University West Lafayette, Indiana 47907, U.S.A. )

The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the ‘elementary disturbances’: plunge, pitch, and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.


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