Bifurcations of gyroscopic systems near a 0 : 1 resonance

Controllability and Observability of Distributed Gyroscopic Systems

10.23919/acc.1990.4790999 ◽

1990 ◽

Author(s):

B. Yang ◽

C. D. Mote

Keyword(s):

Controllability And Observability ◽

Gyroscopic Systems

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On the admissibility of application of precession equations of gyroscopic systems

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(74)90058-6 ◽

1974 ◽

Vol 38 (2) ◽

pp. 204-208

Author(s):

D.R. Merkin

Keyword(s):

Gyroscopic Systems

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Stability of Gyroscopic Systems Near Vanishing Eigenvalues

Journal of Applied Mechanics ◽

10.1115/1.2791903 ◽

1998 ◽

Vol 65 (4) ◽

pp. 1062-1064 ◽

Cited By ~ 2

Author(s):

A. A. Renshaw

Keyword(s):

System Parameter ◽

Degree Of Freedom ◽

Independent System ◽

Physical Systems ◽

Gyroscopic Systems ◽

Two Degree Of Freedom

Renshaw and Mote (1996) proposed a conjecture concerning the growth of vibrating eigensolutions of gyroscopic systems in the neighborhood of a vanishing eigenvalue when the system operators depend on an independent system parameter. Although the conjecture was not proved, it was supported by several examples drawn from well-known continuous physical systems. Lancaster and Kliem (1997), however, recently presented three two-degree-of-freedom counter examples. Unlike the examples tested by Renshaw and Mote (1996), these counter examples lack a definiteness property that is usually found in models derived from physical systems which appears to be essential to the conjecture. This Brief Note revises the original conjecture to include this definiteness criterion and proves the conjecture for general two-degree-of-freedom systems.

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Physical Properties of Transfer Function Zeros for Collocated Control in Flexible Structure System

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0467 ◽

1995 ◽

Author(s):

Chingyei Chung ◽

Chin-yuh Lin

Keyword(s):

Transfer Function ◽

Circulatory System ◽

Flexible Structure ◽

Structure System ◽

Zero Dynamic ◽

Damping Matrix ◽

Generalized Force ◽

Function Zeros ◽

Gyroscopic Systems ◽

Collocated Control

Abstract In this paper, the physical meaning of transfer function zeros for collocated control in a general flexible structure system is discussed. For a flexible structure system, we propose the “Zero Dynamic Theorem”. The theorem states that in a flexible structure system, the flexible structure can be a circulatory system (non-sysmetric stiffness matrix) with viscous and gyroscopic damping (non-symmetric damping matrix), if the sensor output (generalized displacement) and the actuator input (generalized force) are “dual type” and the transfer function is strict proper and coprime (no pole/zero cancellation); then, the transfer function zeros are the natural frequencies of constrained structure. Furthermore, with this theorem, the interlacing pole/zero property for the gyroscopic systems is presented.

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