"Summed and Differential Harmonic" Oscillations in Symmetrical Nonlinear Systems

Abstract

In the present paper, the author verifies analitically and experimentally that "summmed and differential harmonic" oscillations can take place in multiple-degree-of-freedom systems with symmetrical nonlinear spring characteristics, and that only summed type can appear and differential type cannot occur. This "summed and differential harmonic" oscillation consisits of two vibrations with frequencies ω_i and ω_j which are almost equal to the natural frequenies p_i and p_j respectively, and it appears at the frequency ω of the external force which satisfies the relation [numerical formula]. Obtained response curves by experiments are those of hard spring type with jump phenomena.