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Model reduction of large structural dynamic models using proper orthogonal decomposition.

机译：使用适当的正交分解对大型结构动力学模型进行模型归约。

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摘要

This work considers use of Proper Orthogonal Decomposition (POD) to obtain reduced order dynamic models of nonlinear structural systems. The study applies POD to simulated time series data to extract dominant "modes" that describe the system behavior. The "POD modes" are used to formulate reduced order differential equation models (ROM's) of the structure in which the dependent variables are the POD modal coordinates. The objective of this process is to improve the accuracy of the reduced order model while keeping the whole process computationally inexpensive. In quest of this objective, simulations were conducted for a variety of cases for several nonlinear systems.;Three approaches that appear to be new are proposed in this work: (1) development of a "correction matrix" allowing a reduced model to be extended to changed system parameters. The results are shown for a chain of oscillator problem having twenty degrees of freedom; (2) use of band limited random excitation to generate responses from which the POD modes are obtained. Two example systems are considered: (a) a clamped beam whose tip is placed between attracting magnets; POD analysis of this system was done by Kerschen and Feeny [1] using harmonic excitation to excite chaotic motions, which were analyzed to develop the POD modes for reduced order modeling, and (b) a chain of oscillators having an isolated nonlinear Duffing element. (3) a new Ritz vector that is used to augment the POD modes. Results are shown for a fixed-free chain of oscillator system with isolated nonlinearity.
机译：这项工作考虑使用适当的正交分解（POD）来获得非线性结构系统的降阶动力学模型。这项研究将POD应用于模拟的时间序列数据，以提取描述系统行为的主要“模式”。 “ POD模式”用于制定结构的降阶微分方程模型（ROM），其中因变量是POD模态坐标。此过程的目的是提高降阶模型的准确性，同时使整个过程在计算上不昂贵。为了实现这一目标，对几种非线性系统的各种情况进行了仿真。这项工作中提出了三种新的方法：（1）开发“校正矩阵”，从而可以简化模型的扩展。更改系统参数。结果显示了具有二十个自由度的一连串振荡器问题。 （2）使用频带有限的随机激励来生成响应，从中获得POD模式。考虑了两个示例系统：（a）夹持梁，其尖端位于吸引磁体之间；该系统的POD分析是由Kerschen和Feeny [1]使用谐波激励来激发混沌运动进行的，该运动被分析以开发用于降阶建模的POD模式，以及（b）具有隔离非线性Duffing元素的振荡器链。 （3）一种新的Ritz向量，用于增强POD模式。显示了具有孤立非线性的振荡器系统的无固定链的结果。

著录项

  • 作者

    Kumar, Nishant.;

  • 作者单位

    New Mexico State University.;

  • 授予单位 New Mexico State University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 153 p.
  • 总页数 153
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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