时滞惯性流形在三维壁板颤振数值分析中的应用

梅冠华; 张家忠

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时滞惯性流形在三维壁板颤振数值分析中的应用

更新时间：2025-07-09

- 时滞惯性流形在三维壁板颤振数值分析中的应用
- Numerical Analysis of 3-D Panel Flutter by Inertial Manifolds with Delay
- 西安交通大学学报 2011年45卷第9期页码：40-46
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2011-03-30. 作者简介: 梅冠华(1984-),男,博士生;张家忠(联系人),男,教授,博士生导师. 基金项目: 新世纪人才支持计划资助项目(NCET-07-0685)
- DOI：
  中图分类号： O323
- 网络首发：2011-09-10，
  
  纸质出版：2011
- 稿件说明：
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梅冠华, 张家忠. 时滞惯性流形在三维壁板颤振数值分析中的应用[J]. 西安交通大学学报, 2011,45(9):40-46.

Numerical Analysis of 3-D Panel Flutter by Inertial Manifolds with Delay[J]. 2011, 45(9): 40-46.
梅冠华, 张家忠. 时滞惯性流形在三维壁板颤振数值分析中的应用[J]. 西安交通大学学报, 2011,45(9):40-46. DOI：

Numerical Analysis of 3-D Panel Flutter by Inertial Manifolds with Delay[J]. 2011, 45(9): 40-46. DOI：

摘要

应用时滞惯性流形(IMD)对三维壁板颤振问题进行了数值分析.采用von Karman几何大变形理论和一阶活塞理论分别描述平板变形和气动力

由此给出了系统的非线性偏微分控制方程; 采用基于IMD的非线性Galerkin方法

将控制方程的解投影到由其线性算子的特征函数所张成的完备空间内

并截取有限阶模态来逼近真实解

从而将原无穷维动力系统近似为有限维动力系统; 根据IMD思想

构造了反映高、低阶模态关系的时滞表达式

使得在数值模拟过程中无需通过复杂数值积分即可直接获取高阶位移分量

从而降低了系统维数

缩减了计算量; 对系统的平面稳定、屈曲失稳、极限环振动和非简谐周期振动进行了详细分析

求取了平面稳定区域边界.与传统Galerkin方法(TGM)的比较表明

IMD能够达到TGM的计算精度

并使计算时间缩减了7%～11%

说明IMD具有高效、省时的特性

可广泛应用于多自由度耗散型动力系统的求解.

Abstract

The inertial manifolds with delay(IMD)was applied to analyze numerically the three-dimensional panel flutter problem. First

the von Karman's large deformation theory and the first-order piston theory were used to describe the panel deformation and the aerodynamic load

respectively

and the nonlinear partial differential governing equations of the system were presented. Then the IMD based nonlinear Galerkin method was employed to project the solutions of the governing equations onto the complete space spanned by the eigenfunctions of equations' operators. With the truncation of modes to approach the solution

the original infinite dimensional dynamic system is approximated to a finite one. Further

a time-delay expression which implies the interaction between higher and lower modes was constructed. With the time-delay expression presented

the higher displacement modes can be obtained directly without a complicated numerical integration

resulting in a system with less degree-of-freedoms and the reduction of computation time. Finally

four typical steady states of the system were analyzed with the method

and the system flat stable boundary was calculated. The comparison between the IMD and traditional Galerkin method(TGM)shows that IMD has the same accuracy and reduces the computation time by 7%-11%. It is likely that the method presented can be applied to other dissipative dynamic systems with large degree-of-freedoms.

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references

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