Frequency-Amplitude Relationship in Nonlinear Oscillators with Irrational Nonlinearities

Ji-Huan He

doi:10.31181/smeor21202535

Authors

Ji-Huan He School of Jia Yang; Zhejiang Shuren University, Hangzhou; Zhejiang, China Author https://orcid.org/0000-0002-1636-0559

DOI:

https://doi.org/10.31181/smeor21202535

Keywords:

Nonlinear oscillator, Irrational nonlinearity, Frequency-amplitude relationship, Complex dynamics, Mathematical modeling

Abstract

This study investigates the frequency-amplitude relationship in nonlinear oscillators with irrational nonlinearities, which pose significant challenges to traditional analytical methods such as the homotopy perturbation method and variational iteration method. By employing a simplified frequency formulation, we analyze the impact of irrational nonlinearities on oscillation dynamics and derive a frequency-amplitude relationship in a single-step calculation. For small amplitudes, our results are consistent with those obtained by the homotopy perturbation method, validating the proposed approach. This research provides new insights into the complex dynamics of nonlinear oscillators and offers practical implications for fields such as physics, engineering, and applied mathematics. Additionally, it contributes to the design and optimization of MEMS systems and suggests future research directions, including the incorporation of damping and external forces for a more comprehensive understanding of system behavior.

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