FORCED VIBRATION ANALYSIS OF EULER-BERNOULLI BEAM WITH DISCONTINUITIES BY MEANS OF DISTRIBUTIONS WITHOUT DOING MODAL ANALYSIS

Abstract eng:
The general equation of motion of forced vibration of Euler-Bernoulli beam has been used since it was derived by means of classical derivatives of shear force, bending moment, rotation of a cross section and deflection of the beam. However these derivatives are not defined at such points of center-line between ends of the beam in which there is a concentrated load or a concentrated support or a concentrated mass or a concentrated mass-moment of inertia or an internal hinge connecting beam segments, which are discontinuities that can be in practice. In this paper, distributional derivative for discontinuous shear force, discontinuous bending moment, and discontinuous rotation of a cross section of the beam has been applied to derive a generalized mathematical model for forced transverse vibration covering all the discontinuities mentioned. General closed-form solution to the generalized mathematical model for prismatic beam has been computed by means of symbolic programming approach via MAPLE. As a result of this new analytic approach, when computing forced steady-state response of the beam, we do not have to put together any continuity conditions at discontinuity points mentioned. The response of the beam is expressed directly without doing modal analysis.

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