Occurrence of the Summed and Differential Harmonic Oscillations in a Nonlinear Multidegree-of-Freedom Vibratory System

Abstract

Simultaneous occurrence of several oscillations with frequencies ωr (≒pr ) is sometimes observed in a nonlinear multidegree-of-freedom damped vibratory system subjected to harmonic excitation of frequency ω, when the frequency ω and the natural frequencies pr (r = 1, 2, [[ellipsis]], k) of a corresponding undamped linearized system satisfy the condition Nω = Σr=1 k mr pr , in which N is a positive integer and mr are positive or negative integers. Theoretical investigations on the occurrence of such oscillations are carried out for vibratory systems with nonlinear spring characteristics derivable from a potential. The analysis shows that in these systems only the summed type of oscillations with all mr positive have the possibility of occurrence, while the differential type of oscillations with some mr negative do not.