Influence of a finite strain on vibration of a bounded Timoshenko beam

Nicolas Bideau , Loïc Le Marrec (1) , Lalaonirina Rakotomanana-Ravelonarivo (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The goal of this work is to study the eigenmodes of shearable beams with initial finite strain. A three dimensional model is developed on the base of Cosserat continuum mechanics. The characteristics of waves propagation superimposed upon finite pre-stress are obtained using the (rigorous) calculation of the Hamiltonian action. The results are applied on vibration of beam supporting a finite longitudinal strain. Nonlinear effect according to the pre-stress is obtained for various boundary conditions and through a nondimensional formalism

Mots clés: Timoshenko beam; Modal analysis; Pre-stress; Vibrations

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

Nicolas Bideau, Loïc Le Marrec, Lalaonirina Rakotomanana-Ravelonarivo. Influence of a finite strain on vibration of a bounded Timoshenko beam. International Journal of Solids and Structures, 2011, 48 (16-17), pp.2265-2274. ⟨10.1016/j.ijsolstr.2011.02.007⟩. ⟨hal-00610444⟩