Asymptotic Approaches to Study the Mathematical Models of Nonlinear Oscillations of Movable 1D Bodies

The mathematical models of oscillatory systems for describing nonlinear oscillation of the free elastic one-dimensional bodies have been formulated and investigated using asymptotic approaches. The models consider the non-linearity of elastic properties of the body approximated by polynomial functions. Furthermore, the influence of a number of physical, mechanical and kinematical factors on the wave process are considered. The oscillation amplitude and frequency in non-resonant case were obtained as a time-dependent functions. The analytical presentations of system key parameters were obtained for the body’s low speed of movement and homogeneous boundary conditions. The practical use of developed asymptotic approaches to the analysis of technical systems and in engineering practice was pointed out.