Asymptotic Study of Longitudinal Velocity Influence and Nonlinear Elastic Characteristics of the Oscillating Moving Beam

Mathematical models of the nonlinear transversal oscillations for a beam moving along its axis have been studied. These models deal with the nonlinearity of body elastic properties and with the influence of physical–mechanical and kinematic parameters on the oscillation amplitude and frequency of the moving one-dimensional nonlinear systems as well. A procedure for studying both cases, non-resonance and resonance oscillation regimes, has been developed. The paper focuses on the influence of the longitudinal velocity, nonlinear elastic material properties, and external periodical perturbations on the dynamical process of beam transversal oscillation. The obtained mathematical model could be applied to describe the oscillation behavior of the different types of pipelines (liquid or gas). The proposed results allow the estimation of the influence of these parameters on the amplitude and frequency of the oscillations. Mathematical analysis realized by asymptotic methods enables the prediction of the resonance phenomena and proposal of a numerical algorithm to plan the most effective operation regime. Applications of this approach in engineering, particularly to construct the corresponding elements of industrial environments and pipelines, are also discussed.