Combination tones in the response of single degree of freedom systems with quadratic and cubic non-linearities

摘要: Abstract The method of multiple scales is used to analyze the response a single-degree-of-freedom system either combination resonance additive type Ω 2 + 1 ≈ ω 0 or difference − , where and are frequencies excitation ω0 linear undamped natural frequency system. To second approximation, has three effects on steady state response. First, it produces terms having at first order 0, 2Ω 2(Ω ), order. Second, shift in Third, virtual primary-resonant that makes component be rather than Similar produced by superharmonic two.