Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry
- Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry
- 장선준; 김준우; 최용제
- screw theory; geometrical relation of modes; plane of symmetry; vibration of rigid body
- Issue Date
- Proceedings of the Institution of Mechanical Engineers. Part C, Mechanical engineering science
- VOL 226, NO 5, 1254-1262
- 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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