Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems

[+] Author and Article Information
B. Yang

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

J. Appl. Mech 59(3), 650-656 (Sep 01, 1992) (7 pages) doi:10.1115/1.2893773 History: Revised March 01, 1991; Received July 17, 1991; Online March 31, 2008


In his famous treatise The Theory of Sound , Rayleigh enunciated an eigenvalue inclusion principle for the discrete, self-adjoint vibrating system under a constraint. According to this principle, the natural frequencies of the discrete system without and with the constraint are alternately located along the positive real axis. Although it is commonly believed that the same rule also applied for distributed vibrating systems, no proof has been given for the distributed gyroscopic system. This paper presents several eigenvalue inclusion principles for a class of distributed gyroscopic systems under pointwise constraints. A transfer function formulation is proposed to describe the constrained system. Five types of nondissipative constraints and their effects on the system natural frequencies are studied. It is shown that the transfer function formulation is a systematic and convenient way to handle constraint problems for the distributed gyroscopic system.

Copyright © 1992 by The American Society of Mechanical Engineers
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