采用非线性Galerkin方法的柔性梁模型降阶研究

满兴博 1; 伍晓红 2; 孙清 1

doi:10.7652/xjtuxb201507019

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采用非线性Galerkin方法的柔性梁模型降阶研究

更新时间：2025-07-09

- 采用非线性Galerkin方法的柔性梁模型降阶研究
- Study on the Model Order Reduction of Flexible Beam Based on Nonlinear Galerkin Method
- 西安交通大学学报 2015年49卷第7期页码：113-119
- 作者机构：
  
  西安交通大学土木工程系,西安,710049
- 作者简介：
- 基金信息：
  
  : 2014-12-29。作者简介: 满兴博(1992—),男,硕士生;孙清(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(11172226)
- DOI：10.7652/xjtuxb201507019
  中图分类号： TH117.5
- 网络首发：2015-07-10，
  
  纸质出版：2015
- 稿件说明：
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满兴博 1, 伍晓红 2, 孙清 1. 采用非线性Galerkin方法的柔性梁模型降阶研究[J]. 西安交通大学学报, 2015,49(7):113-119.

Study on the Model Order Reduction of Flexible Beam Based on Nonlinear Galerkin Method[J]. 2015, 49(7): 113-119.
满兴博 1, 伍晓红 2, 孙清 1. 采用非线性Galerkin方法的柔性梁模型降阶研究[J]. 西安交通大学学报, 2015,49(7):113-119. DOI： 10.7652/xjtuxb201507019.

Study on the Model Order Reduction of Flexible Beam Based on Nonlinear Galerkin Method[J]. 2015, 49(7): 113-119. DOI： 10.7652/xjtuxb201507019.

摘要

针对采用Galerkin方法获取的结构动力学降阶模型精度不高的问题

以考虑几何非线性的两端固支柔性梁作为研究对象

建立了两端固支柔性梁非线性动力学模型。首先采用Galerkin方法将原系统降阶

得到单自由度、三自由度和五自由度系统

再采用非线性Galerkin方法将二自由度和三自由度系统降阶为单自由度系统。通过分析降阶模型的非线性动力学行为

得到系统响应随外荷载幅值变化的分岔图

给出系统做周期运动、倍周期运动和混沌时的时程曲线、相图与庞加莱映射图。在特定频率下

通过改变外荷载幅值来控制系统进出混沌状态。与Galerkin方法得到的降阶模型进行了对比

通过比较进出混沌状态时的外荷载幅值

分析了两种方法的降阶效果。结果表明:非线性Galerkin方法能够有效提高降阶模型的精度

更接近真实模型; 采用非线性Galerkin方法降阶得到相同自由度的低阶系统时

原模型阶数越高

得到的低阶模型越精确。

Abstract

A nonlinear dynamics model of a flexible beam clamped at both ends is established

and the order of the model is reduced using nonlinear Galerkin method to solve the problem of low accuracy using common Galerkin method. On this basis

the nonlinear dynamical behaviors of the reduced-order model are analyzed

and the bifurcation diagram of system response is obtained when the external load amplitude changes. The time-displacement curves

phase diagrams and Poincare maps are drawn when the system is put in periodic motion

quasi-periodic motion and chaotic motion. Experimental results show that the reduced-order model using nonlinear Galerkin method has higher accuracy than common Galerkin method

especially when the original model has a relatively high order.

关键词

Keywords

references

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