Latest revision as of 09:53, 16 June 2017

Abstract

A general theory for the dynamic analysis of thin walled open beams taking into account shear deformability, variable cross-sectional properties and initial stresses is presented. The present approach, which is based on a general variational formulation of the theory of elasticity, allows the determination, in a unified fashion, of the governing unidimensional variatiotial equation of motion of the beam and the constitutive relations for the stress resultants. The niotion differential equations are then obtained. It is developed a finite element formulation based on the present theory, which is used for detemining natural frequencies of vibrations. Independent determinations are performed for sirriply supported thin walled open beams by means of an analytical solution of the present differential equations. Numerical experiments are done to show the importance of the considered effects and to assess the accuracy of the proposed finite element.

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