Treyssede F.

For thin structures such as beams or plates, the effects of prestress are likely to have a significant impact upon 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 natural frequencies of flexural vibration increase (resp. decrease) when the axial load is tensile (resp. compressive). Nevertheless, most of studies found in the litterature deal exclusively with in-plane prestress effects, whereas prestressed states may generally additionnally include some prebending, yielding a predeformed geometry. To the author knowledge, prebending effects are hardly studied and often neglected, particularly for low prestress states, so that their effects upon vibrations remain obscure. In this paper, linear vibrations of prestressed planar beams including prebending effects are studied. Without loss of generality, this paper focus on thermal prestressing, which is one of the most common sources of stressing. A typical application is given by a bridge subjected to climatic thermal variations, this example being of primary interest in the context of health monitoring based on modal diagnosis with thermal compensation. A finite element beam model is first proposed. The assumption of small prestrains and large predisplacements is made. The model is based upon a total Lagrangian formulation because prebending terms appear explicitly in equilibrium equations, thus giving more insight from a physical point of view. Some numerical results highlighting prebending effects are then given. A validation through experiments inside a climatic chamber is also considered. The main conclusion of this work is that prebending effects – in addition to well-known in-plane prestressing effects – are also likely to be significative upon some eigenfrequencies, even in the case of rather small predisplacements.