Study on solutions of non-linear dynamic equation on ULF standard vibrator

This paper gives out two kinds of approximate analytical solution, non-resonance solution and resonance solution, of non-linear dynamic equation based on a type of Ultra-Low Frequency (ULF) vibrator. Then the paper draws a conclusion through analyzing the format of the result and changing the coefficient of the equation. Study shows that non-resonance solution can present the relationship among amplitude, phase and frequency very Well and can easily obtain all the harmonic's amplitudes on the strong damping condition. Though the solution cannot, reveal the phenomenon that a non-linear equation may have several results corresponding to same frequency on the weak damping condition. At the same time, resonance solution can account for the relationship among amplitude, phase and frequency very well no matter on strong damping condition or on weak damping, condition, but it is very difficult to attain all the harmonic's amplitudes. The research of this paper will provide theory basis for design structure data of the ultra-low frequency vibrator, which want to have minimum waveform distortion.