THE CUSP CATASTROPHE AND THE STABILITY PROBLEM OF HELICOPTER GROUND RESONANCE

被引：7
作者：
AFOLABI, D [1 ]
机构：
[1] PURDUE UNIV,DEPT MECH ENGN,INDIANAPOLIS,IN 46202
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1993年 / 441卷 / 1912期
关键词：
D O I：
10.1098/rspa.1993.0069
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Catastrophe theory is used to derive closed form expressions for the critical speeds of helicopters in ground resonance. The results are obtained for an adaptation of Coleman's model of helicopters with soft, in-plane hingeless rotors. It is shown that the characteristic polynomial of the rotorcraft system is diffeomorphic to a versal unfolding of the cusp catastrophe germ. Expressions are computed for the equilibrium manifold and the bifurcation set. The expression for the bifurcation set is then used to obtain a frequency equation for finding the exact critical speeds.
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页码：399 / 406
页数：8
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