| 引用本文: | 刘雪峰,凡友华,常冬梅.黏弹性层状介质中瑞雷波的本征值求解[J].哈尔滨工业大学学报,2017,49(4):122.DOI:10.11918/j.issn.0367-6234.201508085 |
| LIU Xuefeng,FAN Youhua,CHANG Dongmei.Eigenproblem of Rayleigh wave in multilayered viscoelastic medium[J].Journal of Harbin Institute of Technology,2017,49(4):122.DOI:10.11918/j.issn.0367-6234.201508085 |
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| 摘要: |
| 为解决黏弹性层状介质中瑞雷波本征值求解中的漏根问题，提出了一种新的求解方法.通过分析以往方法中漏根和多根的原因，提出采用一系列初值虚部进行搜根后将结果合并，并去掉虚部大于实部的根.由此给出了本征值求解的流程图，在实例计算中采用此方法成功求解了黏弹性层状介质中瑞雷波的本征值.结果表明，在利用该方法在求解过程中不存在漏根和多根问题.在黏弹性层状介质中瑞雷波的本征值求解时采用搜根初值加密并剔除虚部大于实部的根的方法可以有效避免漏根和多根问题.
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| 关键词: 瑞雷波 黏弹性 层状介质 本征值问题 优化 |
| DOI：10.11918/j.issn.0367-6234.201508085 |
| 分类号:O347.4 |
| 文献标识码:A |
| 基金项目:国家自然科学基金 (41204042)；中央高校基本科研业务(3122015D009)；中国民航大学科研启动基金(2014QD03S) |
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| Eigenproblem of Rayleigh wave in multilayered viscoelastic medium |
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LIU Xuefeng1,2,FAN Youhua1,CHANG Dongmei3
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(1.School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, Guangdong, China; 2.School of Aeronautical Engineering, Civil Aviation University of China, Tianjin 300300, China; 3. Tianjin Key Laboratory of High Speed Cutting and Precision Machining(Tianjin University of Technology and Education), Tianjin 300222, China)
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| Abstract: |
| To avoid the root lost problem in the former methods, a new method of solving the eigenproblem of Rayleigh wave in multilayered viscoelastic medium. The reason of root-lost and pseudo-root phenomenon is analyzed. From this, a series of different initial imaginary parts are employed, and the roots whose imaginary part is larger than real part are omitted. A flowchart of solving the eigenproblem is presented based on this, and the eigenproblem of Rayleigh wave in multilayered viscoelastic medium in an example is successfully solved with the method. The results show that there is no root-lost and pseudo-root phenomenon when solving the eigenproblem with the method. In the eigenproblem of Rayleigh wave in multilayered viscoelastic medium, root-lost and pseudo-root phenomenon can be avoided by employing a series of different initial imaginary parts and omitting the roots whose imaginary part is larger than real part.
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| Key words: Rayleigh wave viscoelastic multilayered medium eigenproblem optimization |
