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

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.