Time domain Green functions for the homogeneous Timoshenko beam

In English In this paper a wave splitting technique is applied to a homogeneous Timoshenko beam. The purpose is to obtain a diagonal equation in terms of the split fields. These fields are calculated in the time domain from an appropriate set of boundary conditions. The fields along the beam are represented as a time convolution of Green functions with the excitation. The Green functions do not depend on the wave fields but only on the parameters of the beam. Green functions for a Timoshenko beam are derived, and the exponential behaviour of these functions as well as the split modes are discussed. A transformation that extracts the exponential part is performed. Some numerical examples for various loads are presented and compared with results appearing in the literature.