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

Abstract

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.

Keywords

diagonalizable stiffness mode decoupling planes of symmetry linear vibration theory of screws

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