Abstract:Through multiple scale method, analyses characteristics of amplitude-frequency response of Duffing system. Multi-frequency excitation changes the main resonance domain of Duffing system under the single-frequency excitation , and the main resonance curve of the system shifts. Through analysis, we can see that multi-frequency excitation amplitude and frequency decide the change extent of Duffing system amplitude-frequency curve. Through numerical simulation, the example of the hard spring Duffing system is calculated, the results show that the multi-frequency excitation change the vibration state of Duffing system under single-frequency excitation. The vibration state of system under different paramaters of multi-frequency excitation are compared , and the theoretical analyses are verified with numerical simulation.