To the investigation of oscillations describing the generalized differential rayleigh equation

Abstract

The study considers the motion of an oscillatory system with one degree of freedom, which is described by the generalized Rayleigh differential equation. The generalization is achieved by replacing the cubic term, which expresses the dissipative force in the equation of motion, with a power term with an arbitrary positive exponent. The method of energy balance is used to study the oscillatory process. With its help, an approximate differential equation of the envelope graph of the oscillatory process is compiled and its analytical solution is obtained, from which it follows that quasilinear frictional selfoscillations are possible only when the exponent is greater than one.