Engineering Mechanics

Proceedings Vol. 21 (2015)

ENGINEERING MECHANICS 2015

Copyright © 2015 Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, v.v.i., Prague

 

J. Sobotka
pages 286 - 287, full text

The general equations of motion for forced vibration of Timoshenko beam have been used since they were derived assuming there were not any discontinuities in the shear force, the bending moment, the cross-section rotation and the deflection of the beam. However in practice, computing harmonic response of the beam, we encounter concentrated loading, concentrated supports, hinges connecting beam segments, concentrated masses or concentrated moments of inertia all of which may be situated between ends of the beam. The definition of the distributional derivative is chosen in order that all the cases causing jump discontinuities in the shear force or the bending moment or the cross-section rotation can be incorporated. As a result of this approach, more general equations of motion for forced vibration of Timoshenko beam implying all jump discontinuities mentioned are presented in this paper. An analytic closed-form solution to the system of equations is found with integration constants in the form of initial parameters. Making use of this approach, we can find exact expression for the harmonic steady-state response of the uniform beam without summing infinite series and without doing a modal analysis of the beam.

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