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.
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Yue Shen (2020) studied this question.
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