Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

S. J. Jang, J. W. Kim, Yong Je Choi

Research output: Contribution to journalArticle

2 Citations (Scopus)


The geometrical properties of vibration modes of a single rigid body with one plane of symmetry are presented. When in-plane vibration modes are represented by the axes normal to the plane of symmetry, three intersecting points of those axes and the plane of symmetry constitute two triangles whose orthocentres are coincident with the mass centre and planar couple point, while the induced wrenches of three out-of-plane modes are found to form two triangles whose orthocentres are lying on the mass centre and the perpendicular translation point. Examining these triangles reveals that the triangular areas are proportional to the distributions of the mass and stiffness in the vibrating system and the shapes of the triangles are related to the natural frequencies. A numerical example is provided to verify the proposed findings.

Original languageEnglish
Pages (from-to)1254-1262
Number of pages9
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Issue number5
Publication statusPublished - 2012 May 1


All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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