| 矩形截面固体波导中弹性导波模式的板波叠加解 |
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| 引用本文： | 凤飞龙, 沈壮志, 沈建中, 卢超. 矩形截面固体波导中弹性导波模式的板波叠加解[J]. 声学学报, 2018, 43(5): 779-785. DOI: 10.15949/j.cnki.0371-0025.2018.05.007 |
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| 作者姓名： | 凤飞龙 沈壮志 沈建中 卢超 |
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| 作者单位： | 1. 陕西师范大学物理学与信息技术学院 陕西省超声学重点实验室 西安 710119; |
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| 基金项目： | 国家自然科学基金项目(11204227,11674207,11774212)资助 |
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| 摘 要： | 参照板中兰姆波模式的子波叠加解求解了矩形截面固体波导中弹性导波的模式。其中子波设定为横向满足自由边界反射条件、纵向波数分量相同的各板波模式。假设声场的完备性,利用子波模式的正交性,结合矩形截面的几何对称性可以得到4组独立导波特征方程用于频散曲线以及导波模式计算,其计算结果与有限元法计算结果相符。研究以解析模型表明:矩形截面固体波导中的导波是其内部以一定纵向波数分量斜向传播的板波模式在两个自由侧面上经过反复反射与模式转化后,横向耦合谐振而形成的。
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| 关 键 词： | 导波模式矩形截面波叠加波导固体弹性板计算结果 |
| 收稿时间： | 2017-05-10 |
| 修稿时间： | 2017-07-23 |
Guided modes in an elastic rectangular bar: solution based on partial plate mode decomposition |
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| FENG Feilong, SHEN Zhuangzhi, SHEN Jianzhong, LU Chao. Guided modes in an elastic rectangular bar: solution based on partial plate mode decomposition[J]. ACTA ACUSTICA, 2018, 43(5): 779-785. DOI: 10.15949/j.cnki.0371-0025.2018.05.007 |
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| Authors: | FENG Feilong SHEN Zhuangzhi SHEN Jianzhong LU Chao |
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| Affiliation: | 1. Shaanxi Key Lab of Ultrasonics, Shaanxi Normal University Xi'an 710062;2. Institute of Acoustics, Chinese Academy of Sciences Beijing 100190;3. Key Laboratory of Nondestructive Testing, Nanchang Hangkong University Nanchang 330063 |
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| Abstract: | Similar to Auld's solution for Lamb waves, the wave modes in elastic rectangular bar are solved by partial wave decomposition method. The partial waves are composed of plate modes with the same wavenumber component in waveguide longitudinal direction, thus free boundary conditions on one pair of opposite surfaces are automatically satisfied. Based on completeness assumption and orthogonality of the plate modes, four independent eigen-equations are eventually derived for dispersion curve and mode shape investigation. Numerical evaluation shows the calculated results are in consistent with the FEM results. It is then verified that the plate modes which obliquely bounced back and forth between the two opposite surfaces compose the guided modes traveling in the rectangular waveguides. |
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