The geometrical mode analysis of a vibrating system with the planes of symmetry

Byung Ju Dan; Yong Je Choi

doi:10.1115/DETC99AZIB-8120

The geometrical mode analysis of a vibrating system with the planes of symmetry

Byung Ju Dan, Yong Je Choi

Department of Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A niimerical example of an application to the vibration analysis of an optical disc drive has been presented.

Original language	English
Title of host publication	17th Biennial Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
Pages	1361-1369
Number of pages	9
ISBN (Electronic)	9780791819777
DOIs	https://doi.org/10.1115/DETC99AZIB-8120
Publication status	Published - 1999
Event	ASME 1999 Design Engineering Technical Conferences, DETC 1999 - Las Vegas, United States Duration: 1999 Sep 12 → 1999 Sep 16

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	7A-1999

Conference

Conference	ASME 1999 Design Engineering Technical Conferences, DETC 1999
Country/Territory	United States
City	Las Vegas
Period	99/9/12 → 99/9/16

Bibliographical note

Publisher Copyright:
Copyright © 1999 by ASME

All Science Journal Classification (ASJC) codes

Mechanical Engineering
Computer Graphics and Computer-Aided Design
Computer Science Applications
Modelling and Simulation

Access to Document

10.1115/DETC99AZIB-8120

Cite this

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title = "The geometrical mode analysis of a vibrating system with the planes of symmetry",

abstract = "Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A niimerical example of an application to the vibration analysis of an optical disc drive has been presented.",

author = "Dan, {Byung Ju} and Choi, {Yong Je}",

note = "Publisher Copyright: Copyright {\textcopyright} 1999 by ASME; ASME 1999 Design Engineering Technical Conferences, DETC 1999 ; Conference date: 12-09-1999 Through 16-09-1999",

year = "1999",

doi = "10.1115/DETC99AZIB-8120",

language = "English",

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booktitle = "17th Biennial Conference on Mechanical Vibration and Noise",

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Dan, BJ & Choi, YJ 1999, The geometrical mode analysis of a vibrating system with the planes of symmetry. in 17th Biennial Conference on Mechanical Vibration and Noise. Proceedings of the ASME Design Engineering Technical Conference, vol. 7A-1999, American Society of Mechanical Engineers (ASME), pp. 1361-1369, ASME 1999 Design Engineering Technical Conferences, DETC 1999, Las Vegas, United States, 99/9/12. https://doi.org/10.1115/DETC99AZIB-8120

The geometrical mode analysis of a vibrating system with the planes of symmetry. / Dan, Byung Ju; Choi, Yong Je.

17th Biennial Conference on Mechanical Vibration and Noise. American Society of Mechanical Engineers (ASME), 1999. p. 1361-1369 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7A-1999).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A niimerical example of an application to the vibration analysis of an optical disc drive has been presented.

AB - Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A niimerical example of an application to the vibration analysis of an optical disc drive has been presented.

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The geometrical mode analysis of a vibrating system with the planes of symmetry

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All Science Journal Classification (ASJC) codes

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