Dynamics of a three-mass system with cubic nonlinearity and that of an equivalent electrical circuit

Abstract

The paper considers the reaction of a mechanical system of three masses connected by springs and absorbers moving in the longitudinal direction to the action of a harmonic force applied to the largest mass. This mass is attached to the base by a spring with cubic nonlinearity, while smaller masses are connected to the main mass by linear springs. A method is proposed for obtaining the amplitude-frequency characteristic (AFC) of a nonlinear system from the AFC sequence of linearized systems. The results of modelling an equivalent electrical circuit, which is an analogue of a mechanical system, are presented. The influence of the value of the nonlinearity coefficient on the dynamic response of systems has been studied. It is noted that for some combinations of values of the system parameters with cubic nonlinearity with mass ratios m1:m2:m3 = 4:2:1, the AFC contains outer and inner isolated areas – islands.