Subharmonic vibrations of order 1/2, and almost periodic oscillations of a nonlinear vibrating system with a restoring characteristic of the Duffing type and a retardation

Abstract

The entrained subharmonic vibrations of order 1/2 of a nonlinear retarded system, with an external force, are investigated by making use of the averaging method. It is also clarified that almost periodic vibrations may occur in the same frequency region where the entrained oscillations appear. These two kinds of vibrations are studied numerically using mapping plots in the phase plane. The analytical results agree well with the numerical solutions and the results from an analog computer simulation.