Prebending effects upon the vibrational modes of thermally prestressed planar beams

Abstract

In this paper, the linear vibrations of thermally prestressed beams are studied including the effects of predisplacement due to prebending and initial imperfections. Only low prestressed states far from the buckling stage are considered, one of the motivations of this paper being the issue of taking into account climatic temperature effects in damage detection based on modal techniques. A brief general review is first presented in order to give some theoretical and physical insights upon structural vibrations superimposed on an initial static state. Both the total Lagrangian and the updated Lagrangian formulations are applied to a planar Euler–Bernouli beam under the assumption of small prestrains and large predisplacements. The governing equilibrium equations are solved using a finite element method. Some illustrative numerical results are given. The model is then validated through experiments inside a climatic chamber. It is concluded that in addition to the axial prestress, the presence of prebending is also likely to have a significant effect upon some eigenfrequencies, even in the case of rather small predisplacements.