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MINI REVIEW article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1579671
This article is part of the Research Topic Nonlinear Vibration and Instability in Nano/Micro Devices: Principles and Control Strategies View all 15 articles
Dynamic analysis of the fractal nonlinear oscillators with coordinate-dependent mass
Provisionally accepted- 1 Jiangxi College of Applied Technology, Ganzhou, China
- 2 Jiangxi University of Science and Technology, Ganzhou, Jiangxi Province, China
- 3 Hunan Institute of Science and Technology, Yueyang, China
The dynamic behavior of nonlinear oscillators can be researched more accurately in the micro-scale. In this paper, a modified nonlinear oscillator with coordinate-dependent mass by He's fractal derivative is first given. Then, the energy balance method and modified harmonic balance method are utilized to constructed the first-order and second-order approximate solutions of the fractal model. Next, two sets of parameters are choosen, the obtained numerical solution are compared with the Runge-kuta (RK) solution, and the results demonstrate that the second-order approximate solution is more accurate. In addition, by comparing the solutions under the different fractal dimensions, one can be found that the fractal dimension does not change global properties of the oscillators, but the vibration behaviors gradually accelerates with the increase of the fractal dimension, which means that we can study the oscillation behavior more clearly in the micro-scale.
Keywords: Nonlinear oscillators, He's Fractal Derivative, Two-scale theory, the energy malance method, the modified harmonic balance method
Received: 19 Feb 2025; Accepted: 26 Mar 2025.
Copyright: © 2025 Ling, Liao and Wu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Pinxia Wu, Hunan Institute of Science and Technology, Yueyang, China
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