Motion of a motor-structure non-ideal system

Abstract

Abstract In this paper the generalization to dynamics of a nonlinear oscillator excited with a non-ideal source is studied. The model of the structure-motor system is generalized by assuming that the driving torque is a nonlinear function of the angular velocity and the oscillator is with strong nonlinearity. The oscillator-motor system is assumed as a non-ideal one where not only the motor affects the motion of the oscillator but also vibrations of the oscillator have an influence on the motor motion. The model of the motor-structure system is described with two coupled strong nonlinear differential equations. An improved asymptotic analytic method based on the averaging procedure is developed for solving such a system of strong nonlinear differential equations. The steady state motion and its stability is studied. Results available the discussion of the Sommerfeld effect. A new procedure for determination of parameters of the non-ideal system for which the Sommerfeld effect does not exist is developed. For these critical values of the parameter the Sommerfeld effect is suppressed. As a special case the truly nonlinear oscillator where the order of the nonlinearity is a positive rational number is investigated. In the paper the influence of the order of nonlinearity on the dynamic properties of the system are analyzed. For the motor, with the torque which is the cubic function of the angular velocity, and the truly nonlinear oscillator, with certain order of nonlinearity, the numerical calculation is done. Analytically obtained results are compared with numerical ones. Results show good agreement.