| 童韫哲,范军,王斌.Floquet-Bloch理论在频散曲线计算中的应用[J].声学技术,2020,39(1):11~14 |
| Floquet-Bloch理论在频散曲线计算中的应用 |
| Application of Floquet-Bloch theory in dipersion curve calculation |
| 投稿时间：2019-06-07 修订日期：2019-08-10 |
| DOI：10.16300/j.cnki.1000-3630.2020.01.002 |
| 中文关键词: Lamb波 频散曲线 波有限元法 Floquet-Bloch理论 周期性边界条件 |
| 英文关键词: lamb wave dispersion curve Wave Finite Element(WFE) method Floquet-Bloch theory periodic condition |
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| 中文摘要: |
| 实现了一种基于波有限元方法计算无限大平面波导中弹性波频散曲线的方法。该方法在有限尺度计算单元两边添加Floquet-Bloch周期性边界条件来近似模拟无限大弹性平面波导，利用有限元Comsol Multiphysics软件计算波导中弹性波频散曲线，并讨论了有限尺度单元长宽之比与计算频段的关系。计算结果与谱方法计算结果对比，吻合很好，验证了方法的有效性。该方法回避了复杂特殊函数计算以及超越方程求解的困难，具有建模和计算简单的优点，并可推广至其它复杂弹性波导频散曲线的计算。 |
| 英文摘要: |
| The Floquet-Bloch theory based on Wave Finite Element (WFE) method for dispersion curve calculation is described in this paper. In the method, the periodic condition of Floquet-Bloch theory adds on both sides of the finite scale calculation cell to approximately simulate an infinite elastic wave guide. The elastic wave dispersion curves in a plane waveguide are obtained by using the commercial Finite Element software ‘COMSOL Multiphysics’. The calculation results obtained by WFE method and spectral method are in good agreement. And, the influence of R (the length to width ratio of the calculation cell) on the correct region of the result is discussed. This method has the advantages of easy modeling and simple calculation due to avoiding the difficulties of calculating complex special functions and solving the complex transcendental equation. This method can also be extended to calculating the dispersion curves of other more complex waveguides. |
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