Locus of the axis of vibration for a vibrating system with variable location of a mass center

A typical approach to a linear vibration analysis of an elastically supported single rigid body is to rearrange a dynamic model into a corresponding eigenvalue problem. From the geometrical point of view, the eigenvectors in the planar vibration analysis can be interpreted as pure rotations about the vibration center or pure translations. In a three dimensional space, they represent repetitive twisting motions about the axes of vibrations. By taking a geometrical approach to the vibration analysis, the vibration mode shapes may be better understood. In this paper, the influence of variable location of a mass center on the locations of the axes of vibrations and the natural frequencies are investigated by means of the locus of the axis of vibration expressed in analytical form, which represents the geometrical locus of the eigenvector. A numerical example is used to clearly illustrate the vibration phenomena of an optical pick-up used in an information storage device.