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The Fourier spectral element method for vibration and power flow analysis of complex dynamic systems.

机译：用于复杂动力系统振动和功率流分析的傅立叶谱元方法。

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摘要

A general numerical method, the so-called Fourier-Space Element Method (FSEM), is proposed for the vibration and power flow analyses of complex built-up structures. In a FSEM model, a complex structure is considered as a number of interconnected basic structural elements such as beams and plates. The essence of this method is to invariably express each of displacement functions as an improved Fourier series which consists of a standard Fourier cosine series plus several supplementary series/functions used to ensure and improve the uniform convergence of the series representation. Thus, the series expansions of the displacement functions and their relevant derivatives are guaranteed to uniformly and absolutely converge for any boundary conditions and coupling configurations. Additionally, and the secondary variables of interest such as interaction forces, bending moments, shear forces, strain/kinetic energies, and power flows between substructures can be calculated analytically.;Unlike most existing techniques, FSEM essentially represents a powerful mathematical means for solving general boundary value problems and offers a unified solution to the vibration problems and power flow analyses for 2- and 3-D frames, plate assemblies, and beam-plate coupling systems, regardless of their boundary conditions and coupling configurations. The accuracy and reliability of FSEM are repeatedly demonstrated through benchmarking against other numerical techniques and experimental results.;FSEM, because of its exceptional computational efficacy, can be efficiently combined with the Monte Carlo Simulation (MCS) to predict the statistical characteristics of the dynamic responses of built-up structures in the presence of model uncertainties. Several examples are presented to demonstrate the mean behaviors of complex built-up structures in the critical mid-frequency range in which the responses of the systems are typically very sensitive to the variances of model variables.
机译：提出了一种通用的数值方法，即所谓的傅里叶空间单元法（FSEM），用于复杂结构的振动和功率流分析。在FSEM模型中，复杂结构被视为许多相互连接的基本结构元素，例如梁和板。该方法的本质是将每个位移函数始终表示为改进的傅立叶级数，该傅立叶级数由标准傅立叶余弦级数加上几个补充级数/函数组成，用于确保和改善级数表示的均匀收敛。因此，对于任何边界条件和耦合配置，位移函数及其相关导数的级数展开均被保证均匀且绝对收敛。此外，还可以解析地计算出感兴趣的次要变量，例如相互作用力，弯矩，剪切力，应变/动能以及子结构之间的功率流。;与大多数现有技术不同，FSEM本质上代表了一种强大的数学方法，可以解决一般问题。边界值问题，并为二维和3-D框架，板组件和梁板耦合系统的振动问题和功率流分析提供统一的解决方案，而无需考虑其边界条件和耦合配置如何。通过对其他数值技术和实验结果进行基准测试，反复证明了FSEM的准确性和可靠性。FSEM由于其出色的计算效率，可以有效地与Monte Carlo Simulation（MCS）结合使用，以预测动态响应的统计特征在存在模型不确定性的情况下建立结构的数量。给出了几个示例，以说明在临界中频范围内复杂组合结构的平均行为，在该范围内，系统的响应通常对模型变量的方差非常敏感。

著录项

  • 作者

    Xu, Hongan.;

  • 作者单位

    Wayne State University.;

  • 授予单位 Wayne State University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 236 p.
  • 总页数 236
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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