Sylvester’s eliminant and stability criteria for gyroscopic systems

✍ Scribed by D. Afolabi

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 562 KB
• Volume: 182
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1995.0194

✦ Synopsis

The classical criterion of Routh-Hurwitz is not applicable for stability analyses of undamped vibrating systems. Two new criteria suitable for the linear stability analyses of such systems are presented, one for flutter and the other for divergence. Like the classical criterion, the procedures developed here are based on the characteristic polynomial of a given system. The flutter criterion requires a computation of the discriminant of the characteristic polynomial. Sylvester's dialytic method of elimination is used to compute the required discriminant. The stability criteria presented here may be used not only to obtain flutter and divergence boundaries, but also to identify various instability zones in a parameter space. To demonstrate the effectiveness of the new criteria, applications are made to two problems: the vibration of rotating shafts and of rotating rings. Closed form solutions for stability boundaries are obtained without solving the eigenvalue problems associated with the systems, but from a simpler procedure which utilizes the methods presented in this paper.