本文使用微扰论方法对纸张振动建立非线性动力学方程模型，通过该模型预测纸张产生的低音与高音现象以及它们之间的联系，并通过实验验证.该模型的非线性动力学方程中存在与低音解相关的分数倍频解，这与实验中存在的分数倍频振动现象相吻合.该模型解释了整数倍频高音产生的非线性本征性以及分数频低音与分数倍频高音产生的衍生性，实验结果中的整数振动与分数振动现象满足理论预测.

A nonlinear dynamic equation of paper vibration is established by the perturbation theory method. The relationship between the bass and the treble phenomena is predicted and verified by experiments. There is a fractional octave solution related to the bass solution in nonlinear dynamic equation of the model, which is consistent with the fractional octave vibration phenomenon in experiments. The intrinsic characteristics of integer multiple sizes of harmonic, as well as the derivative of fractional bass and harmonic generation are explained by the model. The integer and fractional vibration in the experiment satisfy the theoretical prediction.