On the 1/2-th Subharmonic Vibrations of a Non-Linear Vibrating System with a Doffing Type Restoring Characteristic : 2nd Report, Soft Spring Case

Abstract

The 1/2-th sub-harmonic oscillations of a system with a Duffing type restoring characteristic are investigated by making use of a harmonic balance method, under the condition that both the periodic exciting force (e, g., an unbalancing force) and the constant force (e.g., gravity) are operative. In contrast with the preceding paper⁽¹⁾, the restoring characteristic of this system is assumed to be a soft spring. As a result, the phenomena of these vibrations are considerably complicated and also extremely different from the same kind of vibrations in the hard spring system⁽¹⁾. However, the occurrence of the 1/2-th sub-harmonic vibrations in this system is possible similar to the hard spring system, even if the constant stimulating force approaches zero.