The 1/2-Subharmonic and Summed-and-Differential Harmonic Oscillations in a Nonlinear Rectilinear Vibratory System : The Variations of Resonance Curves and the Occurrence of Unstable Vibration due to Quartic Nonlinear Terms

Abstract

This paper deals theoretically with a subharmonic oscillation of order 1/2 and some sort of summed-and-differential harmonic oscillations in a rectilinear vibratory system with nonlinear spring characteristics, which are expressed by the terms of the second, third and fourth powers of coordinates. Especially, the effects of quartic terms on these oscillations caused by the nonlinear terms up to the third power of coordinates are investigated. It is clarified that quartic terms have qualitatively different effects from those of quadratic terms, and that unstable vibrations occur due to quartic terms. These kinds of unstable vibrations have been observed experimentally in a rotating shaft system by the authors of this paper.