VIBRATIONS IN A PARAMETRICALLY EXCITED SYSTEM

This paper deals with vibrations of parametrically excited non-linear systems with one degree of freedom. The non-linearity is cubic and is of the same order as the linear terms. The parametric vibrations are excited by a periodical force of Jacobi elliptic type. The mathematical model of the system is a special type of non-linear Hillʹs equation. The analytical approximate solution of the equation is obtained applying the elliptic-Krylov–Bogolubov method (method of variable phase and amplitude) developed for strong non-linear differential equation of Duffing type. It enables the regions of unbounded solution to be defined approximately. The parameters of a dynamic absorber which transforms the motion to regular are calculated in this paper.