Free Vibration Analysis of a Free-Free Single-Tapered Beam Carrying Arbitrary Concentrated Elements Using Modified Mode-Superposition Method (MMSM)

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