一种用于分析某些摆振荡器的创新方法.
Galal M Moatimid1, T S Amer2, Abdallah A Galal3
1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt.
Scientific reports
|May 7, 2025
概括
本研究使用非扰动方法 (NPA) 分析了三种类型的简单 (SPs). NPA为分析机械系统中的非线性动态和稳定性提供了一种新的方法.
科学领域:
- 物理 物理学 物理
- 机械工程 机械工程
- 应用数学 应用数学 应用数学
背景情况:
- 摆振荡器对于理解和运动,节能和非线性动力学至关重要.
- 它们的应用涵盖了各种领域,包括工程,地震学和量子力学.
研究的目的:
- 分析三个不同的简单的摆形 (SP) 系统:带电磁性SP,滚动圆柱体SP和流体流中的化SP.
- 应用非扰动方法 (NPA) 来对非线性动态和稳定性标准进行新的分析.
主要方法:
- 利用基于He的频率公式 (HFF) 的非扰动方法 (NPA) 来线性化非线性普通微分方程 (ODE).
- 使用Mathematica软件 (MS) 对线性模型与非线性ODEs进行数值比较和验证.
- 生成时间历史图和相平面图以分析系统行为和稳定性.
主要成果:
- 在传统的扰动技术上,NPA显示了优势,避免了泰勒扩展,并使稳定性分析成为可能.
- 数字比较显示,NPA的线性化解决方案与原来的非线性ODEs之间有很强的一致性.
- 阶段肖像显示系统稳定性和不稳定性接近平衡点,受磁场和角速度的影响.
结论:
- 非扰动方法 (NPA) 提供了一种精确有效的方法,用于分析简单的摆形系统中复杂的非线性动态.
- 这项研究强调了系统参数 (如磁场) 对摆筒运动和稳定性的影响.
- 这项研究为机械振动和非线性系统的行为提供了宝贵的见解.
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