Vibration design of a rigid body supported by orthogonal springs

Seon Jun Jang, Jun Ho Lee, Yong Je Choi

Research output: Contribution to journalArticle

Abstract

Vibration analysis of a rigid body supported by in-parallel linear springs can be greatly simplified by utilizing the conditions for a plane of symmetry. The vibration modes of an oscillatory system having plane of symmetry are classified into the in-plane and out-of-plane modes. From the viewpoint of screw theory, they represent respectively the vibration axes perpendicular to the plane of symmetry and lying in the plane of symmetry. In this paper, the sets of orthogonal and mutually intersecting three springs are used as resilient support of a rigid body. The geometrical conditions for the system to have aplane of symmetry and diagonalized stiffness matrix are presented. From the orthogonality of the vibration modes with respect to the inertia matrix, the geometrical relation between the reaction wrenches and the vibration modes are derived. This geometrical relation is then used to get the cubic design equation for the design of out-of-plane modes. The numerical design example of engine mounts is presented in order to explain the suggested design technique.

Original languageEnglish
Pages (from-to)97-104
Number of pages8
JournalTransactions of the Korean Society of Mechanical Engineers, A
Volume31
Issue number1
DOIs
Publication statusPublished - 2007 Jan 1

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Hand tools
Stiffness matrix
Vibration analysis
Engines

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

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abstract = "Vibration analysis of a rigid body supported by in-parallel linear springs can be greatly simplified by utilizing the conditions for a plane of symmetry. The vibration modes of an oscillatory system having plane of symmetry are classified into the in-plane and out-of-plane modes. From the viewpoint of screw theory, they represent respectively the vibration axes perpendicular to the plane of symmetry and lying in the plane of symmetry. In this paper, the sets of orthogonal and mutually intersecting three springs are used as resilient support of a rigid body. The geometrical conditions for the system to have aplane of symmetry and diagonalized stiffness matrix are presented. From the orthogonality of the vibration modes with respect to the inertia matrix, the geometrical relation between the reaction wrenches and the vibration modes are derived. This geometrical relation is then used to get the cubic design equation for the design of out-of-plane modes. The numerical design example of engine mounts is presented in order to explain the suggested design technique.",
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Vibration design of a rigid body supported by orthogonal springs. / Jang, Seon Jun; Lee, Jun Ho; Choi, Yong Je.

In: Transactions of the Korean Society of Mechanical Engineers, A, Vol. 31, No. 1, 01.01.2007, p. 97-104.

Research output: Contribution to journalArticle

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