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ABSTRACT

 

The conditions for mode decoupling of a linear vibration system with diagonalizable stiffness matrices via screw theory

 

Hong, Man Bok

Year 2011

 

  In this article, a new geometric approach to the conditions for mode decoupling of an elastically suspended rigid body with a diagonalizable stiffness matrix is presented. The necessary and sufficient condition for diagonalization of a spatial stiffness matrix by a proper co-ordinate transformation is derived using the form of the stiffness matrix expressed by uniquely determined three orthogonal lines and three orthogonal torsional springs. Three orthogonal planes are defined by use of the axes of the line springs. Both the spatial displacements lying on or perpendicular to each of the planes and the spatial forces induced due to the displacements are decoupled into two linearly independent three-systems of screws. From this property and the geometric relations between those planes obtained from the stiffness and the principal planes of inertia, the conditions for mode decoupling of the vibration system are derived and the possible locations of the axes of the decoupled vibration modes are identified.

 

Mechatronics & Robotics Lab at Yonsei Univ., Korea

 

제목
J W Kim, S Lee, Y J Choi, "Design method of planar vibration system for specified ratio of energy peaks," Journal of Sound and Vibration (2015), http://dx.doi.org/10.1016/j.jsv.2015.01.016i
J. W. Kim, M. B. Hong, Y. J. Choi, "New jacobian approach to the kinestatic analysis of a planar double-wishbone suspension mechanism", Proc. IMechE, Part D: Journal of Automobile Engineering, 2013.
S. J. Jang, J. W. Kim, Y. J. Choi, "Triangular relationship between vibration modes of an elastically supported rigid body with a plane of symmetry", Proc. IMechE, Part C: Journal of Mechanical Engineering Science Vol. 226 No. 5 , pp.1254-1262, 2012.
M. B. Hong, Y. J. Choi, "Design method of planar three-degrees-of-freedom serial compliance device with desired compliance characteristics", the Institution of Mechanical Engineers, Mechanical engineering science Vol. 226 No.9, pp.2331-2344, 2012.
M. B. Hong, Y. J. Choi, "Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators", Journal of mechanisms and robotics Vol .3, pp.1-6, 2011.
M. B. Hong, Y. J. Choi, "Design method of planar three-degrees-of-freedom serial compliance device with desired compliance characteristics", The Institution of Mechanical Engineers, Mechanical engineering science Vol. 226 No.9, pp.2331-2344, 2012.
M. B. Hong, Y. J. Choi, "Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators", Journal of mechanisms and robotics Vol .3, pp.1-6, 2011.
M. B. Hong, Y. J. Choi, "The conditions for mode decoupling of a linear vibration system with diagonalizable stiffness matrices via screw theory“, Proceedings of the Institution of Mechanical Engineers. Part C, Mechanical engineering science Vol. 225
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