MODAL INTERACTIONS IN SELF-EXCITED OSCILLATORS UNDER EXTERNAL PRIMARYRESONANCE

The dynamics of two-degree-of-freedom oscillators including Rayleigh a nd Duffing type non-linearities is investigated. The method of multipl e scales is first applied and a set of averaged equations is derived f or cases of primary external resonance. These equations admit two type s of constant solutions. The first type involves the directly excited mode only, while for some parameter combinations the non-linear dampin g terms excite the second mode also, even when no internal resonance i s present. Stability and bifurcation analyses are then presented. Emph asis is placed on deriving explicit conditions on the system parameter s that will lead to forms of the evolution equations which can be stud ied in detail, by utilizing results from the area of dynamical systems . To illustrate the effectiveness and accuracy of the analysis, numeri cal results are presented for a dynamic model of a specific practical system: namely, a three-parameter study is first carried over in order to reveal basic response features of a metal cutting system. Codimens ion one, two and three bifurcations are determined and their effect on the interaction and transition between the response modes is investig ated. A representative sample of response diagrams and results from di rect integration are also presented, providing an overall picture of t he dynamics. (C) 1995 Academic Press Limited