Vibrations of a Forced Self-excited System with a Retarded Argument : Subharmonic Vibrations of Order 1/2

Abstract

The subharmonic entrained vibrations of order 1/2 of a nonlinear retarded system with a soft spring type are investigated by making use of an averaging method, under the condition that both a periodic exciting force and a constant force are operative. The Routh-Hurwitz criterion provides the stability conditions of these steady oscillations. It is also revealed that almost periodic vibrations occur in the same frequency region in which the entrained vibrations appear. These two kinds of oscillations are studied numerically using mapping plots in the phase plane. The analytical results relatively agree with the numerical solutions and the results of an analog computer. In addition, it is shown that the subharmonic oscillations of order 1/2 can take place in the same system, even though there is only a periodic force as the stimulating force.