TY - JOUR

T1 - Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry

AU - Jang, S. J.

AU - Kim, J. W.

AU - Choi, Y. J.

PY - 2012/5

Y1 - 2012/5

N2 - 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.

AB - 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.

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U2 - 10.1177/0954406211422145

DO - 10.1177/0954406211422145

M3 - Article

AN - SCOPUS:84864778315

SN - 0954-4062

VL - 226

SP - 1254

EP - 1262

JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

IS - 5

ER -