On the 1/2-th Subharmonic Vibrations of a Non-linear Vibrating System with a Hard Duffing Type Restoring Characteristic

Abstract

Assuming that both a periodic exciting force (e.g., due to an unbalancing force) and a constant force (e.g., due to gravity) are acting on a nonlinear vibrating system, the 1/2-th subharmonic vibrations of the system with a hard Duffing type characteristic are investigated by making use of an averaging procedure. Furthermore, it is shown that the 1/2-th subharmonic oscillations can take place in the same system, even if there is only a periodic force as the driving force. Analytical results are compared with the results obtained by numerical integration from the same system, carried out by the Runge-Kutta-Gill method. As a result, it appears that the present theory gives relatively satisfactory results in calculating these vibrations.