Forced vibrations of the shaft line based on the model of a two-stage rod with an elastic connection of sections

The paper considers a method for solving the problem of dynamics of forced vibrations of a wall line based on a model of an equivalent elastic two-stage rod with a pliable connection of sections. The model is represented by a system of partial differential equations. The solution of the equations is obtained by the Fourier method for eigenfunctions orthogonal with weight. It is established that the presence of an elastic element at the junction of the sections does not affect the orthogonality of the eigenfunctions. The influence of the elastic coupling compliance coefficient on the natural frequency spectrum of the shaft line is estimated. The obtained forms of natural vibrations of an equivalent elastic two-stage rod are consistent in appearance with the corresponding forms known in the literature for a discrete model of a similar torsional circuit. A partial solution of the equations is found for the case of the action of the harmonic load on the engine and the averaged torque on the propeller. As an example, the dynamics of forced vibrations of the shaft line of a barge of the Sosnovka type is studied. The results of calculating the natural frequencies of the considered model are compared with the classical discrete mass method. The analysis of the obtained plots of the twisting angles and torques showed that the angles are satisfactorily approximated by the first proper oscillation shape, and for moments, high shapes must be taken into account. The comparison of the simulation results with the data of the torsiogram obtained under production testing conditions indicates the need for further development of the model. Further improvement of the torsional circuit, as well as a more detailed study of the nature of the operating loads, are considered as promising areas of research.