The modified single mode method in the investigations of the resonant vibrations of non-linear systems

Abstract

To study the effects of non-linearities on the resonant vibrations of multi-degree-of-freedom systems (lumped parameter or continuous ones) the modified “single non-linear mode” method is presented and the results obtained are compared to those produced by the commonly used classical single mode method. As an illustrative example a three-degree-of-freedom system is examined; the resonance curves are determined by the modified method and by the classical single mode method, and the results are checked by the aid of the analog computer. New effects of the restoring force non-linearity are found, effects which are suppressed by the approximations of the classical single mode method.