Javid's Paradox: The Influence of Preform on the Modes of Vibrating Beams

摘要

A theoretical analysis is presented of a vibratory system in which it is possibleto eliminate an unwanted mode of vibration by using that mode as an initial deformation of the system. The analysis shows that this is possible in straight beams with end restraints in axial deformation. The mathematical problem leads to an eigenvalue problem of a type not normally encountered. In the paper examples are given for the changes in eigenfrequency and mode shape produced by the initial preformed shape of the beam for cases where the preform is proportional to a mode of the straight beam and when the preform is unrelated to any mode. The analysis shows that, while elimination of a mode in the strict sense is not achieved, the results can be interpreted for practical purposes in this way.