This thesis examines the linear dynamic bending and torsion vibrations of a simply supported Bernoulli Euler beam under a moving time varying load with constant velocity. The main target is to nd an analytical solution of the governing partial dierential equations. Those are solved by two dierent solving methods. In a rst step the equations are separated in a time depending and a space depending part by the means of a separation approach to get the eigenmodes of the beam. The rst method of solution applies the method of nite integral transformation. Therefore the partial dierential equation is transformed by use of the generalized nite integral transformation and the resulting parameters are combined. In a next step this equation is transformed by use of the LaplaceCarson integraltransformation. The resulting algebraic equation can now be rearranged and transformed back considering the position of the poles. The second back transformation yields the solution in the time domain. The second method solves the equations by means of eigenmode decomposition. Therefore the partial dierential is converted into an ordinary dierential equation in time under considering the orthogonality of the eigenmodes. After insertion into the underlying separation approach one obtains the solution of the partial dierential equation. Considering the boundary and initial conditions and applying some simplication yields the simplied solution. This solution is investigated under resonance conditions and also the convergence for the number of eigenmodes is established. It is plotted over time and space and the occurring phenomenon are discussed. The rst part of the thesis observes pure bending load only by means of the BernoulliEuler beam theory. Therefore the described methods are used. As a last point the special case of static deection is investigated. ^The second part considers pure torsion deformation only by means of the pure torsion or SaintVenant torsion theory. The described methods for solving the equations are used again. The solution shows a similar structure as the pure bending solution. In the third part, the coupled bending and torsion deformation is considered by two coupled partial dierential equations. In this part, the torsional warping of the beam is considered. The solution is derived by use of modal transformation. The two equations are converted to matrixform by use of the separation approach. The resulting matrices show a benecially allocation. The modal decoupling yields two ordinary dierential equations in time. These are solved with one of the described ways in part one or two. This solution has to be transformed back and leads to the solutions of the coupled equation. These are plotted and the resulting phenomenon are discussed. In the fourth part the analytic solutions are compared to a numerical calculation of a simplied nite element model. This shows good agreement of the two solutions.
