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Mid-frequency dynamic characteristics prediction of thin plate based on B-spline wavelet on interval finite element method

机译：基于B-样条小波的区间有限元法薄板中频动态特性预测

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摘要

Due to low computing efficiency and dispersion errors, Traditional Finite Element Methods (TFEMs) based on general polynomials cannot provide efficient dynamic solutions within mid-frequency domain which is the gap between low and high frequency domain. It is also defined as mid-frequency problem in the field of sound and vibration analysis. To solve this problem, it is essential to overcome these two disadvantages simultaneously based on much better computing efficiency and numerical stability. Fortunately, due to the multi-scale/multi-resolution features, the c1type Wavelet Finite Element Methods (WFEMs) own much better computing efficiency and numerical stability. Therefore, WFEMs will be introduced for dealing with the low computing efficiency and dispersion errors and solving the mid-frequency problem based on multi-element analysis. But, due to the complex nodes numbering and Degree of Freedoms (DOFs) numbering, the c1type WFEMs combined with existing assembling formulas cannot provide efficient solutions by multi-element analysis any more. Therefore, this paper mainly consists of two parts of research work. On the one hand, the proper assembling formulas are derived detailedly based on c1type WFEMs. On the other hand, the method combining c1type B-spline wavelet thin plate element with the newly derived assembling formulas is proposed for predicting dynamic characteristics and solving mid-frequency problem related to thin plate structures. The numerical study shows that both computing efficiency and numerical stability of the proposed method are much better than TFEMs’. Furthermore, the proposed method's prediction ability can break through the limitation of TFEMs’ highest computing accuracy. In addition, the proposed method is verified by experimental study for predicting acceleration Frequency Response Functions (FRFs) of thin plate within 5 Hz–1000 Hz, and the experimental results indicate that the proposed method provides the potential to solve mid-frequency problem related to thin plate structures.
机译：由于低计算效率和色散误差，基于通用多项式的传统有限元方法（TFEM）无法在中频域（即低频域和高频域之间的差距）内提供有效的动态解决方案。在声音和振动分析领域，它也被定义为中频问题。为了解决这个问题，必须基于更好的计算效率和数值稳定性同时克服这两个缺点。幸运的是，由于具有多尺度/多分辨率特性，c1型小波有限元方法（WFEM）拥有更好的计算效率和数值稳定性。因此，将引入WFEM来处理低计算效率和色散误差，并基于多元素分析解决中频问题。但是，由于复杂的节点编号和自由度（DOF）编号，因此c1type WFEM与现有的组装公式结合无法再通过多元素分析提供有效的解决方案。因此，本文主要包括两部分研究工作。一方面，基于c1型WFEM详细推导了正确的装配公式。另一方面，提出了将c1型B样条小波薄板单元与新推导的组合公式相结合的方法，以预测动态特性并解决与薄板结构有关的中频问题。数值研究表明，所提方法的计算效率和数值稳定性均优于TFEM。此外，该方法的预测能力可以突破TFEM最高计算精度的局限性。另外，通过实验研究验证了该方法在5 Hz–1000 Hz范围内预测薄板加速度的频率响应函数（FRF），实验结果表明该方法为解决与振动有关的中频问题提供了可能。薄板结构。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第10期|526-541|共16页
  • 作者

    Jia Geng; Xingwu Zhang; Xuefeng Chen; Chenxi Wang; Jiawei Xiang;

  • 作者单位

    School of Mechanical Engineering, Xi'an Jiaotong University,The State Key Laboratory for Manufacturing Systems Engineering;

    School of Mechanical Engineering, Xi'an Jiaotong University,The State Key Laboratory for Manufacturing Systems Engineering;

    School of Mechanical Engineering, Xi'an Jiaotong University,The State Key Laboratory for Manufacturing Systems Engineering;

    School of Mechanical Engineering, Xi'an Jiaotong University,The State Key Laboratory for Manufacturing Systems Engineering;

    Zhejiang Provincial Key Laboratory of Laser Processing Robot / Key Laboratory of Laser Precision Processing & Detection, Wenzhou University;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Mid-frequency problem; Wavelet finite element methods; Thin plate;

    机译：中频问题小波有限元方法薄板;

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