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We present a dynamic analysis for transverse vibration of a Timoshenko beam supported along its length by an elastic wall (Winkler foundation) and subjected to a longitudinal force that acts in order to have eventually a buckling situation.
We use analytical methods based on bifurcation theory for buckling and modal analysis for vibration rather than numerical methods. Here the beam behaviour is influenced by two control parameters: longitudinal force and the rigidity modulus of the elastic wall.
We observe two regimes according to the ratio γ between the rigidity modulus of the wall and shear and bending modulus. For soft wall (γ<1) the bending effect is negligible and buckling may occur in different form with more than one arch for buckling shape. For specific situation the same critical load may obtain for various buckling shape. This interesting behaviour is presented in details through explicit analysis for various boundary conditions.
