On the Third Superharmonic Resonance in the Duffing Oscillator

摘要: Abstract The third order superharmonic resonance in two versions of a harmonically excited Duffing oscillator is investigated by analytical and numerical methods. It shown that even situations for which non-linear may be thought priori to satisfy the "small perturbation" requirements, results obtained amplitude-expansion method perturbation analysis lead incomplete and/or erroneous results. For excited, oscillators, equivalence approximate solutions fundamentally different schemes questioned: Duffing-Ueda oscillator, it sudden transition into chaos result saddle-node bifurcation response; out boundary crisis.