Eigenvalue Inclusion Principles for Discrete Gyroscopic Systems

[+] Author and Article Information
B. Yang

Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453

J. Appl. Mech 59(2S), S278-S283 (Jun 01, 1992) doi:10.1115/1.2899501 History: Received July 11, 1990; Revised December 20, 1990; Online March 31, 2008


In his famous treatise The Theory of Sound, Rayleigh enunciated an eigenvalue inclusion principle for modified discrete nongyroscopic systems. According to this principle, the natural frequencies of a nongyroscopic system without and with modification are alternatively located along the positive real axis. Although vibration and dynamics of discrete gyroscopic systems have been extensively studied, the problem of inclusion principles for discrete gyroscopic systems has not been addressed. This paper presents several eigenvalue inclusion principles for a class of discrete gyroscopic systems. A transfer function formulation is proposed to describe modified gyroscopic systems. Six types of modifications and their effects on the system natural frequencies are studied. It is shown that the transfer function formulation provides a systematic and convenient way to handle modification problems for discrete gyroscopic systems.

Copyright © 1992 by The American Society of Mechanical Engineers
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