...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Applied Mathematical Modelling >Analytical approximation of weakly nonlinear continuous systems using renormalization group method
【24h】

Analytical approximation of weakly nonlinear continuous systems using renormalization group method

机译：弱非线性连续系统的重归化群法解析逼近

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

A direct method based on renormalization group method (RGM) is proposed for determining the analytical approximation of weakly nonlinear continuous systems. To demonstrate the application of the method, we use it to analyze some examples. First, we analyze the vibration of a beam resting on a nonlinear elastic foundation with distributed quadratic and cubic nonlinearities in the cases of primary and subharmonic resonances of the nth mode. We apply the RGM to the discretized governing equation and also directly to the governing partial differential equations (PDE). The results are in full agreement with those previously obtained with multiple scales method. Second, we obtain higher order approximation for free vibrations of a beam resting on a nonlinear elastic foundation with distributed cubic nonlinearities. The method is applied to the discretized governing equation as well as directly to the governing PDE. The proposed method is capable of producing directly higher order approximation of weakly nonlinear continuous systems. It is shown that the higher order approximation of discretization and direct methods are not in general equal. Finally, we analyze the previous problem in the case that the governing differential equation expressed in complex-variable form. The results of second order form and complex-variable form are not in agreement. We observe that in use of RGM in higher order approximation of continuous systems, the equations must not be treated in second order form.
机译：提出了一种基于重归一化群方法（RGM）的直接方法来确定弱非线性连续系统的解析近似。为了演示该方法的应用，我们使用它来分析一些示例。首先，我们分析了在n阶一次谐波和次谐波谐振情况下，具有非线性分布的二次弹性和三次非线性的弹性基础上的梁的振动。我们将RGM应用于离散控制方程，也直接应用于控制偏微分方程（PDE）。结果与以前使用多尺度方法获得的结果完全一致。其次，我们获得了基于具有分布三次非线性的非线性弹性基础上的梁的自由振动的高阶近似。该方法不仅适用于离散控制方程，也可直接应用于控制PDE。所提出的方法能够产生弱非线性连续系统的直接高阶近似。结果表明，离散化和直接方法的高阶近似通常不相等。最后，在控制微分方程以复变量形式表示的情况下，我们分析了先前的问题。二阶形式和复变量形式的结果不一致。我们观察到在连续系统的高阶逼近中使用RGM时，方程不能以二阶形式处理。

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