Natural vibration frequencies of tapered beams Engineering

Abstract

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.