Non-ideal mechanical system with an oscillator with rational nonlinearity

Abstract

In this paper the generalized form of a non-ideal system which contains a pure nonlinear oscillator and a non-ideal energy source is studied. In the non-ideal oscillator-motor system there is an interaction between the motions of the oscillator and those of the motor, as the motor has an influence on the oscillator and vice versa. The mathematical model of the system is represented with two coupled nonlinear differential equations. The averaging method for solving these differential equations is based on the application of the Ateb function, which is the exact solution of the pure nonlinear oscillator. Using the obtained approximate solution, the resonant motion of the system is considered. Significant attention is paid to the steady-state motion and to the Sommerfeld effect. The influence of the order of nonlinearity on the dynamics of the nonideal system is evident. In the paper the procedure for determination of the parameters for suppression of the Sommerfeld effect of the non-ideal system is also given.