# nonlinear oscillations

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

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

## Method of normal oscillations and substantiation of the choice of parameters for certain nonlinear systems with two degrees of freedom

On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed.  To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane.  The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotatio

## Wave concept of motion in mathematical models of the dynamics of two-dimensional media studying

The methodology of the studying of dynamic processes in two-dimensional systems by mathematical models containing nonlinear equation of Klein-Gordon was developed. The methodology contains such underlying: the concept of the motion wave theory; the single - frequency fluctuations principle in nonlinear systems; the asymptotic methods of nonlinear mechanics. The aggregate content allowed describing the dynamic process for the undisturbed (linear) analogue of the mathematical model of movement.