Normal form transformation and an application to a flutter-type of vibration

On the Stability Analysis of Systems Withinternal Resonance

“…Based on potential #ow models, it can be shown that the fundamental solutions for the velocity potential are exponentially dispersive in the downstream direction and essentially wave-like in the vicinity of the conductor bundle. On this basis a set of appropriate functions are use to model the coe$cients of lift and drag rather than the polynomials used in reference [7]. While a detailed discussion of the accuracy of the modelling is not too relevant to the main thrust of the analysis, a qualitative justi"cation for the approximate model may be provided based on the physics of potential #ows.…”

“…The physically meaningful modelling of these coe$cients is strictly a matter of expediency as it permits the coe$cients to be easily expanded in a Taylor's series without recourse to di!erentiation of numerical approximations to experimentally determined values. Further, as the original data quoted by Kern and Maitz [7] were not available, the approximation route was the only one open to the author.…”

“…The numerical example considered was similar to the one considered by Kern and Maitz [7]. However, not only a di!erent value had to be selected for velocity ratio, b, the aerodynamic lift and drag coe$cients data presented graphically by Kern and Maitz were approximated using di!erent basis functions.…”