Thesis Summary:

In the present work the elastodynamic problem of Timoshenko beams is discussed, starting from a constructive characterization of the equations that describe the behavior of the beam in elastodynamic, adapting results of existence, unicity, regularity and behavior in the limit, in a sense a Need, of our problem (following the Wu line). Subsequently, an experimental study of the blocking phenomenon (a phenomenon to be described later) will be made, through the use of an appropriate numerical method and the interpretation of the results of its implementation. Initially, a brief introduction is developed in which the necessity of the study of this problem is manifested. Then, we introduce the static version of the equations to be studied through a construction based on energy methods and variational principles, in order to establish the dynamic variational problem that we will study in the following. Subsequently, we present results of existence, uniqueness and regularity, based on a priori estimation methods for hyperbolic equations (using tools such as Gronwall inequality) and a result that establishes the relationship between a family of problems (each one of them The already studied but associated to a fixed thickness, as parameter) with a limit problem of said family, namely, the elastodynamic problems of the beam of Timoshenko and Euler-Bernoulli, respectively. In turn, a finite element method is formulated to model the evolutionary problem of Timoshenko, with the use of reduced integration, that will allow to treat the problem without suffering from numerical block. We continue with a first approximation to the a priori estimation of the method error, that of the temporal semidiscretization. By way of illustration, numerical experiments are presented for the validation of the free blocking method and experimental determination of the convergence orders for the same method. Finally, conclusions of this work and future work are presented. A brief appendix is ​​included in which the use of a blocking free method is experimentally justified.