Quasi-Harmonic Bending Waves Evolution in a Beam Lying on the Generalized Nonlinear-Elastic Foundation and Possibility of their Transformation into a Sequence of Wave Packets

Abstract

The paper considers dynamic behavior of a track structure, which is a beam performing bending vibrations and lying on the elastic foundation. In this case, a generalized base model is selected that contains two independent bed coefficients: stiffness for tensile (compressive) and shear deformations. Such a model takes into account the soil distributive ability, i.e., its property to settle not only under the loaded area and the foundation, but also in its vicinity. In addition,to describe the foundation stiffness nonlinear properties, the model assumed dependence on the transverse midline beam and its gradient displacement. Results analysis of the wave processes in the beam showed that, since bending waves had strong dispersion, solution to the problem in the presence of weak nonlinearity was close to solution of a linear problem, and it could be represented as a set of quasi-harmonics. Using the Lighthill criterion, conditions modulation instability manifestation (self-modulation) of the quasi-harmonic waves, which led to their spatial localization and division into separate wave packets, were studied. Analytical expressions were found that described the wave packets shapes. Dependences connecting the amplitude and the wave packet width with the elastic foundation rigidity were analyzed