The Earthquake Engineering Online Archive

Javid's paradox: the influence of preform on the modes of vibrating beams

Kelly, James M.; Sackman, Jerome L.; Javid, Ahmad

UCB/EERC-90/02, Earthquake Engineering Research Center, University of California, Berkeley, 1990-03, 45 pages (525/K44/1990)

A theoretical analysis is presented of a vibratory system in which it is possible to 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 this 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. Results are presented.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-90-02.pdf (1 MB)