Use of the Kernel function in a three-dimensional flutter analysis with application to a flutter-tested delta-wing model

Donald S. Woolston, John L. Sewall
SEP 1958

The development and the numerical application are presented of a Rayleigh-Ritz, or modal, type of flutter analysis which takes into account three-dimensional structural and aerodynamic behavior. The flutter mode is approximated by a series of natural-vibration modes, and the aerodynamic forces corresponding to these modes are derived from subsonic lifting-surface theory, according to the kernel -function approach, for a finite wing oscillating in compressible flow. The application is made to a delta semispan wing with a leading-edge sweep angle of 45 degrees which fluttered at a Mach number of 0.85. Results of flutter calculations show that, for this case, when the first three or four natural-vibration modes are used to approximate the flutter mode, converged solutions for the flutter speed are obtained that are about 5 percent less than the experimental value. Theoretical flutter-speed boundaries were located for a range of densities and Mach numbers including those of the experimental-flutter condition. Further application of the analysis to study the effects of variation in certain structural properties showed that the converged flutter speeds were more sensitive to variations in the natural frequencies than to either variations in mass or to the inclusion of generalized-mass coupling terms whose existence is due to the use of experimental natural mode shapes.

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