Vibration analysis of single rigid-body systems having planes of symmetry

Abstract

By taking a geometrical approach to vibration analysis, the vibration mode shapes of a single rigid body may be better understood. From the geometrical point of view, the eigenvectors represent repetitive twisting motions on the axes of vibrations in a three-dimensional space. The frequency response can be expressed by a scalar multiple of the axis of vibration in Plücker's axis coordinates, which is the reciprocal product of the axis of vibration and applied force. The geometrical interpretation of the frequency response provides the design methodology to eliminate the undesired peaks. The methodology involves making the mutual moment of the axis of vibration and applied force become zero or adjusting the location of the axes of vibrations to the sensing point. In order to implement this geometrical design method, an optical pick-up used in the information storage device has been utilized. Some numerical results show design improvement concerning the frequency response of the pick-up device and thereby the validity of the design technique.