Subharmonic Oscillations in Non-linear Systems

Abstract

This paper deals with the subharmonic oscillations which occur in systems with non-linear restoring force. It is first investigated that the order of the subharmonics has the close connection to the form of the non-linear characteristics. Then the subharmonic oscillation of order 1/3, i.e., the oscillation whose fundamental frequency is one-third that of the applied force, is particularly investigated for the cases in which the non-linear characteristics are expressed by (1) cubic and (2) quintic functions. In both cases the stability problem of the periodic solutions is discussed in detail following the stability criterion given previously by the present author. The analysis has revealed that in the latter case (2) the second higher-harmonc of the subharmonic, i.e., the oscillation of order 2/3 causes the collapse of the original subharmonic oscillation under certain circumstances.