Nonlinear oscillators arise everywhere in engineering, and though there are many analytical methods available, a fast and accurate estimation of the frequency–amplitude relationship is much needed in practical applications. He’s frequency formulation meets this requirement, but the local points are chosen randomly. In this paper, the Gaussian interpolation points are adopted, making He’s method more mathematically rigorous and physically reliable. The cubic-quintic Duffing equation is used for comparison, and an excellent result is obtained.

中文翻译：

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La的Lagrange插值用于He的频率公式

非线性振荡器在工程中无处不在，尽管有许多可用的分析方法，但在实际应用中仍然需要快速，准确地估计频率-振幅关系。他的频率公式满足此要求，但是局部点是随机选择的。在本文中，采用了高斯插值点，使He的方法在数学上更加严格并且在物理上更可靠。使用三次立方Duffing方程进行比较，并获得了极好的结果。