The Consistency between MLP Method and Modified Method of Multiple Scales for Strong Nonlinear Primary Resonance of Duffing Equation Subject to Harmonic Excitation in Complex Number Field

With changing strong nonlinear Duffing equation subject to harmonic excitation with damping in complex number field as an object, the amplitude frequency response equation of primary resonance of the system is obtained through parametric transformation with application of MLP method and modified method of multiple scales. In different approximation solution forms and different time scales, the two methods lead to the same amplitude frequency response equation. Thus, the two methods are mutually verifiable. Numerical analysis shows that for the strong nonlinear Duffing equation with damping in complex number field, the nonlinear stiffness coefficient is more than zero and the amplitude frequency response curve of primary resonance leans to the left, which is different from the weak nonlinear Duffing equation.Chinese books catalog: O321