Numerical and Experimental Study of the Vibrational Modes of Thermally Prestressed and Prebent Beams
نویسنده
چکیده
In this paper, the linear vibrations of thermally prestressed beams are studied, including the prebending effects. General equations governing structural vibrations superimposed on an initial static state are first given. They are applied to a planar Euler-Bernoulli beam under the assumption of small prestrain and large predisplacement. Initial imperfections are included in the whole analysis. The governing equilibrium equations are solved using a finite element method. This model is then validated through experiments inside a climatic chamber. INTRODUCTION For thin structures such as beams or plates, the effects of prestress are likely to have a significant impact upon the structural dynamical behaviour. On the contrary of fully thick structures, this occurs even for relatively low prestress states, far from the buckling stage, because of an amplifying factor given by the slender ratio. As far as beams are concerned, it is well known that the natural frequencies of flexural vibration increase (resp. decrease) when the axial load is tensile (resp. compressive) [1]. Nevertheless, most of studies found in the litterature deal exclusively with inplane prestress effects, whereas prestressed states generally induce some prebending, yielding a predeformed geometry. To the author knowledge, the prebending effects are hardly studied and often neglected, particularly for low prestress states, so that their effects upon vibrations remain obscure. In this paper, the linear vibrations of prestressed planar beams including prebending effects are studied. Without loss of generality, this paper focus on thermal prestressing, in the context of structural health monitoring based on modal diagnosis with thermal compensation [2] and the need of ha l-0 06 39 66 1, v er si on 1 9 N ov 2 01 1 Author manuscript, published in "International Congress on Sound and Vibration, France (2006)"
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