PROPERTIES OF NONLINEAR OSCILLATIONS OF DISSIPATIVE MECHANICAL SYSTEMS WITH A LIMITED NUMBER OF DEGREES OF FREEDOM

Abstract

This article studies nonlinear oscillation processes of dissipative mechanical systems with a limited number of degrees of freedom. The properties of dissipative forces, their influence on nonlinear oscillations, the stability of oscillations, the formation of limit cycles, subharmonic and superharmonic resonance phenomena are analyzed. Also, the main mechanisms of nonlinear oscillations are considered using spatial portraits, Lyapunov stability criteria, parametric oscillations, Duffing, Van der Pol and Rayleigh-type models. The energy balance of systems, the effect of the degree of dissipation on the time evolution of the oscillation amplitude are also covered from a mathematical point of view.