| Mindlin板条中弹性波传播问题的分析 |
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| 引用本文： | 胡超,韩刚,房学谦,黄文虎.Mindlin板条中弹性波传播问题的分析[J].应用数学和力学,2006,27(6):701-708. |
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| 作者姓名： | 胡超 韩刚 房学谦 黄文虎 |
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| 作者单位： | 1. 哈尔滨工业大学,航天学院,哈尔滨,150001;同济大学,航空航天与力学学院,上海,200092
2. 哈尔滨工业大学,航天学院,哈尔滨,150001 |
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| 摘 要： | 基于Mindlin弹性厚板理论，采用Hamilton状态空间求解方法，研究了板条横向两侧为自由边界条件下的弹性：波传播问题，给出了问题的分析解，以及各种振动模态和波传播模的存在性．采用本征函数展开法给出了条形板中导波模的频散方程，并与直接根据Mindlin提出的解获得的频散关系进行了比较，通过比较发现：在短波时，频散曲线相差较大，即前几阶低频模式有一定差别。根据Hamilton体系得到的截止频率高一些，长波时频散曲线几乎相同，即高频模式无差别。
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| 关 键 词： | Mindlin厚板 结构导波 Hamilton体系 频散关系 行波控制 扩展模与局部振动模 |
| 文章编号： | 1000-0887（2006）06-0701-08 |
| 收稿时间： | 2005-01-27 |
| 修稿时间： | 2006-02-23 |
Flexural Wave Propagation in Narrow Mindlin's Plate |
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| HU Chao,HAN Gang,FANG Xue-qian,HUANG Wen-hu.Flexural Wave Propagation in Narrow Mindlin''''s Plate[J].Applied Mathematics and Mechanics,2006,27(6):701-708. |
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| Authors: | HU Chao HAN Gang FANG Xue-qian HUANG Wen-hu |
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| Institution: | 1. School of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China; 2. School of Aerospace Engineering and Mechanics, Tongji University,Shanghai 200092, P. R. China |
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| Abstract: | Appling Mindlin's theory of thick plates and Hamilton formulism to propagation of elastic waves under free boundary condition,a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method.It was compared with the dispersion relation that was gained through solution of thick plate theory proposed by Mindlin.Based on the two kinds of theories,the dispersion curves show great difference in the region of short waves,and the cutoff frequencies are higher in Hamiltonian systems.However,the dispersion curves are almost the same in the region of long waves. |
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| Keywords: | Mindlin's plate wave propagation Hamilton formulism dispersion relation control of traveling wave extended wave and localized vibration |
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