周期结构有限元分析的时域方法

S. Ballandras, V. Laude, S. Clatot, M. Wilm
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引用次数: 1

摘要

对于具有短脉冲响应的振动结构或波导,时域分析是谱域计算的一个有趣的替代方法。我们提出了一个允许解决周期性暂态问题的发展。对于谐波计算,我们只对阵列的一个周期进行网格化,然后应用其边缘相互关联的边界条件。定义了一个类似于谱域的周期激励系数,并用于扫描所有可能的激励图。然后展示了如何推导描述阵列的不同单元耦合在一起的方式的相互时域系数。值得注意的是,在这种时域表示中,计算信号上没有出现奇点,这为推导互系数提供了非常有利的条件。但是没有一个考虑综合周期边界条件。本文提出了一种求解周期暂态问题的方法。在谐波计算的情况下,我们只网格阵列的一个周期,然后我们应用周期边界条件。定义了一个与谱域相似的周期激励系数,并用于扫描所有可能的激励情况。时间激励用狄拉克(或Heaviside)脉冲表示。然后展示了如何推导相互时域系数,描述阵列的不同单元耦合在一起的方式。值得注意的是,在这种时域表示中,计算信号中没有出现奇点,这为推导互系数提供了非常有利的条件。对于大多数读者来说,这种时域表示可能更容易理解,并且应该为具有低质量因子的大规模周期性器件的表征提供有效的方法。第一部分专门介绍所采用的集成方案的基本原理,即纽马克方法。然后报告了2-2压电复合材料结构的结果,以及在真空中操作的2D微机械超声换能器(MUT)的情况。由于声在这些结构中传播引起的串扰现象是通过推导它们的相互参数(导纳,前速度)来确定的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A time domain approach for the analysis of periodic structures using finite element analysis
The time domain analysis is an interesting alternative to spectral domain computations for vibrating structures or wave-guides exhibiting short impulse responses. we propose a development allowing for solving periodic transient problems. As for harmonic computations, we mesh only one period of the array and we then apply boundary conditions relating its edges one another. A periodic excitation coefficient similar to the one used in the spectral domain is defined and use to scan all the possible excitation figures. It is then shown how to derive mutual time domain coefficients that describe the way the different cells of the array are coupled together. It is remarkable that in this time domain representation, no singularity arises on the computed signals, yielding very favourable conditions for the derivation of mutual coefficients. but none take into account comprehensive periodic boundary conditions. In this paper, we propose a method to solve periodic transient problems. As in the case of harmonic computations, we mesh only one period of the array and we then apply periodic boundary conditions. A periodic excitation coefficient similar to the one employed in the spectral domain is defined and is used to scan all possible excitation situations. The time excitation is represented by Dirac (or Heaviside) impulses. It is then shown how mutual time domain coefficients can be derived that describe the way the different cells of the array are coupled together. It is remarkable that in this time domain representation, no singularities arise in the computed signals, resulting in very favourable conditions for the derivation of mutual coefficients. This time domain representation may be more accessible for most readers and should provide an efficient approach for the characterization of massively periodic devices with low quality factors. The first section is devoted to the fundamentals of the adopted integration scheme, i.e. the Newmark approach. Results are then reported in the case of a 2-2 piezocomposite structure and also in the case of a 2D micro-machined ultrasonic transducer (MUT) operating in a vacuum. Cross-talk phenomena due to acoustic propagation in these structures are identified thanks to the derivation of their mutual parameters (admittance, front velocity).
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