Engineering Transactions, 57, 1, pp. 45–66, 2009

Natural vibration frequencies of tapered beams Engineering

Faculty of Engineering Department of Structural Engineering, (DiSGG)

Faculty of Architecture Department of CoMMA

In this paper the free vibrations frequencies of tapered Euler-Bernoulli beams are calculated,
in the presence of an arbitrary number of rotationally and/or axially, elastically flexible
constraints. The dynamic analysis is performed by means of the so-called cell discretization
method (CDM), according to which the beam is reduced to a set of rigid bars, linked together
by elastic sections, where the bending stiffness and the distributed mass of the bars is concentrated.
The resulting stiffness matrix and mass matrix are easily deduced, and the generalized
symmetric eingenvalue problem can be immediately solved. Various numerical comparisons
allow us to show the potentialities of the proposed approach.
Keywords: free vibrations, tapered beam, elastically restrained, CDM
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