In this paper, a highly accurate analytical approximation solution method to a class of mixed-parity Duffing equation is proposed. The system may be attributed to the free vibration of laminated anisotropic plates or the simplified problem of particle vibration. The system is first analyzed qualitatively and subsequently, the analytic approximate periodic solution within the parametric range is constructed. The first approximate solution with a suitable initial condition can be obtained by using the proposed method. Subsequently, higher precision approximate solutions are constructed by combining Newton’s method and harmonic balance method. These analytical solutions have excellent approximation accuracy as verified by numerical solutions derived from exact analytical expressions.

中文翻译：

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混合奇偶杜芬方程的高精度解析近似解

本文提出了一类混合奇偶杜芬方程的高精度解析逼近求解方法。该系统可能归因于层压各向异性板的自由振动或粒子振动的简化问题。首先对系统进行定性分析，然后构造参数范围内的解析近似周期解。利用该方法可以得到具有合适初始条件的一阶近似解。随后，结合牛顿法和调和平衡法，构造出精度更高的近似解。这些解析解具有出色的近似精度，这已通过从精确解析表达式得出的数值解得到验证。