Forced Oscillations of System with Nonlinear Restoring Force

Abstract

Integrating numerically the Duffing Equation
(Remark: Graphics omitted.),
the periodic solutions and the response curves have been studied for hard system (β≥0). Peculiar behaviors of the accurate response curves are found—the existence of the higher harmonic resonances of odd order, where the response curves have loops, and those of even order, where the response curves have branches accompanied with loop. As k approaches zero, the loops expand infinitely. As k increases, the loops change into simple maximums which vanish finally as well as the branches.
For vanishing k the subharmonic resonances of any integral and fractional order have been found so far as trials have been done. They vanish when k increases or β approaches zero under positive k. Also the linear limits of the responses are considered.