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Technical Brief

Modal Analysis of the Gyroscopic Continua: Comparison of Continuous and Discretized Models

[+] Author and Article Information
Xiao-Dong Yang

Beijing Key Laboratory of Nonlinear Vibrations
and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China
e-mail: jxdyang@163.com

Song Yang

Beijing Key Laboratory of Nonlinear Vibrations
and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China
e-mail: 554634456@qq.com

Ying-Jing Qian

Beijing Key Laboratory of Nonlinear Vibrations
and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China
e-mail: candiceqyj@163.com

Wei Zhang

Beijing Key Laboratory of Nonlinear Vibrations
and Strength of Mechanical Engineering,
College of Mechanical Engineering,
Beijing University of Technology,
Beijing 100124, China
e-mail: sandyzhang0@yahoo.com

Roderick V. N. Melnik

M2NeT Laboratory,
The MS2Discovery Interdisciplinary Research Institute,
Wilfrid Laurier University,
75 University Avenue West,
Waterloo, ON N2L 3C5, Canada
e-mail: rmelnik@wlu.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 17, 2016; final manuscript received May 31, 2016; published online June 16, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 83(8), 084502 (Jun 16, 2016) (5 pages) Paper No: JAM-16-1089; doi: 10.1115/1.4033752 History: Received February 17, 2016; Revised May 31, 2016

The vibrations of gyroscopic continua may induce complex mode functions. The continuous model governed by partial differential equations (PDEs) as well as the discretized model governed by ordinary differential equations (ODEs) are used in the dynamical study of the gyroscopic continua. The invariant manifold method is employed to derive the complex mode functions of the discretized models, which are compared to the mode functions derived from the continuous model. It is found that the complex mode functions constituted by trial functions of the discretized system yield good agreement with that derived by the continuous system. On the other hand, the modal analysis of discretized system demonstrates the phase difference among the general coordinates presented by trial functions, which reveals the physical explanation of the complex modes.

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Figures

Grahic Jump Location
Fig. 2

Comparison of the mode functions by continuous and discretized methods: (a) the first mode and (b) the second mode

Grahic Jump Location
Fig. 1

The snapshots of the axially moving material during modal motions: (a) the first modal motions and (b) the second modal motions

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