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Contribution to the free vibration problem of a free‐free beam with large end masses
Author(s) -
Šalinić Slaviša,
Obradović Aleksandar,
Dunjić Momčilo,
Sekulić Dragan,
Lazarević Željko
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600300
Subject(s) - beam (structure) , vibration , physics , boundary value problem , eccentricity (behavior) , transverse plane , transverse vibration , mechanics , classical mechanics , mathematical analysis , mathematics , structural engineering , optics , acoustics , engineering , political science , law
Free vibration of an Euler‐Bernoulli beam with rigid bodies connected to the beam ends by both revolute joints and torsional springs is considered. The mass centers of rigid bodies have both the transverse and the axial eccentricity relative to the neutral axis of the undeformed beam. The coupling of the partial differential equations of axial and bending vibrations of the beam due to boundary conditions is considered. The frequency equation and the mode shape orthogonality condition of the system are derived. In order to illustrate the effect of the transverse and the axial eccentricity on the vibration behavior of the beam, a numerical example is provided.