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HIGH-FREQUENCY VIBRATION ANALYSIS 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的薄板高频振动分析。

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For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can't be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on cl type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0~1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.
机译:对于薄板弯曲问题的动态分析,有限元方法(FEM)是工程中最常用的数值技术。但是由于有限的计算效率和准确性,有限元法不能直接用于有效地评估低高频范围内具有高模态密度的薄板的动力分析。为了解决这个问题,本文提出了小波有限元方法(WFEM)来解决该问题,以提高计算效率和准确性。由于多分辨率的特性,WFEM具有极高的计算效率和结构分析的准确性。此外,针对预测薄板在高频域内的动态响应的目的,本文介绍了一种基于cl型小波薄板单元的多小波单元方法和一种新的组装程序,旨在显着提高计算效率和精度。在使用现有WFEM和传统FEM时打破了频域限制。此外,通过一个特殊的具有高模态密度的数值例子,通过数值研究证明了该方法的有效性,该方法通过预测0〜1000Hz范围内的薄板状态响应来验证该方法的有效性。根据文献,针对数值示例,0至1000Hz之间的频域包含低高频域。数值结果表明分别与有限元法和解析表达式所获得的参考解决方案吻合。其中,值得注意的是,当动态响应涉及1000个模式时,解析解和数值解之间的相对误差小于0.4%。

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