Study of the dynamic process in a nonlinear mathematical model of the transverse oscillations of a moving beam under perturbed boundary conditions

Abstract

The study of transverse oscillations of systems moving along their axis is a very difficult, but at the same time a very important task. Mathematical models of nonlinear transverse oscillations of a beam moving along its axis are analyzed in this paper work, both for non-resonant and resonant cases. The task becomes even more complicated if we additionally take into account the method of fastening the ends of the beam or the perturbation at its ends. We have obtained dependencies that can be used in construction, transport, industry, mechanical engineering and other domains of technology, ensuring the stability and safety of the operation of such mechanical systems. Mathematical models have been obtained for structural engineers to determine the amplitude–frequency response of relevant structures. These mathematical models are key to researching the dynamics of moving media. The obtained results allow considering not only the influence of kinematic and physical-mechanical parameters on the amplitude–amplitude frequency response of the medium, but also the fastening method. In addition, the correlations obtained in the paper make it possible to study not only the influence of the moving medium parameters on the nature of changes in the frequency and amplitude of oscillations, but also to consider the movement at the points of support of the medium. Namely, even at the stage of designing a pipeline for a liquid flowing at a certain speed, it is possible to consider the influence of the oscillation of the supports or their fastening method on the dynamics of the oscillatory process. The resulting dependencies allow designers to consider the influence of the characteristics given in the paper with a high level of accuracy and predict dynamic phenomena in them. In engineering calculations of various mechanical systems, the resulting dependencies can be used to optimize parameters to avoid negative destructive phenomena during operation.