Jang, J. Kim, J. W. Choi, Y. J. 2024-01-20T15:00:46Z 2024-01-20T15:00:46Z 2022-01-10 2012-05 0954-4062 https://pubs.kist.re.kr/handle/201004/129276 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. English SAGE PUBLICATIONS LTD Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry Article 10.1177/0954406211422145 1 PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE, v.226, no.C5, pp.1254 - 1262 PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 226 C5 1254 1262 scie scopus 000305535400010 2-s2.0-84864778315 Engineering, Mechanical Engineering Article screw theory geometrical relation of modes plane of symmetry vibration of rigid body