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Abstract

The literature contains scant information on the free vibration analyses of the loaded single-tapered beams (STBs) (i.e., STBs carrying concentrated elements (CEs)) Furthermore, even when such studies have been performed, they generally only consider the case of constrained (e.g., free-clamped (F-C)) beams. In other words, the problem of unconstrained (e.g., free-free (F-F)) loaded STBs has not yet to be addressed. Thus, the present study employs the modified mode-superposition method (MMSM) to investigate the free vibration characteristics of the F-F loaded STB carrying arbitrary various CEs. The investigation focuses particularly on the natural frequencies and mode shapes of the rigid-body motions and elastic vibrations of the STB. The presented MMSM differs from the conventional mode-superposition method (CMSM) in that the mode shapes of the rigid-body motions of the F-F bare STB are also taken into account, whereas the CMSM considers only the elastic vibration of the STB. The numerical results show that, for the considered F-F loaded STB problem, the CMSM provides neither any information regarding the rigid-body motions of the beam, nor any satisfactory solutions for the elastic vibrations. The correctness of the presented theory and developed computer code is demonstrated by comparing the numerical results obtained using the proposed MMSM with those obtained from the finite element method (FEM). It is shown that the two sets of results are in good agreements.

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