• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >Approximate fully analytical Fourier series solution to the forced and damped Helmholtz-Duffing oscillator
【24h】

Approximate fully analytical Fourier series solution to the forced and damped Helmholtz-Duffing oscillator

机译：强迫和阻尼亥姆霍兹-达芬振荡器的近似完全解析傅里叶级数解

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We obtain improved approximate fully analytical steady state solutions for the ordinary differential equation of the forced and damped anharmonic oscillator with quadratic and cubic nonlinearities. The solutions, are obtained in the form of a truncated Fourier series using the harmonic balance method (HBM). In order to obtain explicit analytical expressions for the Fourier coefficients we introduce the hypothesis of weak interdependence between the equations in the system of nonlinear algebraic equations produced by the HBM. Comparison with the numerical solution shows that the analytical results for the first harmonics which we investigated are valid in comparatively strong nonlinear regimes, where previously obtained expressions are completely inaccurate. Our expressions are correct over a wide range of the physical parameters, such as excitation frequency, nonlinearity and forcing. The proposed method of solution is expected to be suitable for other nonlinear ordinary differential equations.
机译：对于具有二次和三次非线性的强迫和阻尼非谐谐振子的常微分方程，我们获得了改进的近似全解析稳态解。使用谐波平衡法（HBM）以截短傅立叶级数的形式获得解。为了获得傅立叶系数的明确解析表达式，我们介绍了由HBM产生的非线性代数方程组中方程之间的弱相互依赖关系的假设。与数值解的比较表明，我们研究的一次谐波的分析结果在相对强的非线性条件下是有效的，在这种情况下，先前获得的表达式完全不准确。我们的表达式在各种物理参数上都是正确的，例如激励频率，非线性和强迫。所提出的解决方法有望适用于其他非线性常微分方程。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号