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Vibration of Elastically Coupled Cantilever Beams using Greens's Functions

Department of Mechanical Engineering, King Abdulaziz University, PO Box 80204, Jeddah 21589, Saudi Arabia

Abdulghaffar A N Al-Jawi

The dynamic characteristics of cantilever beams, elastically coupled into linear and cyclic chains are considered theoretically, using Green's functions. This leads to finite difference equations, which can be solved easily for the tuned structure, or to tri-diagonal and cyclic tri-diagonal matrices for the linear and cyclic chains respectively, when mistuning is present, which can be inverted by standard routines. Free wave propagation and forced vibrations are both studied. Propagation constants for the tuned problem are presented and discussed. Mode localization factors are determined using Monte Carlo simulation when mistuning is introduced. The finite element code (ABAQUS) is also applied in the determination of natural frequencies and the study of free mode localization.

Key Words: Green's functions • mode localization • cyclic chains • mistuned

Journal of Vibration and Control, Vol. 9, No. 11, 1303-1324 (2003)
DOI: 10.1177/1077546304030673


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