| 功能梯度材料梁自由振动问题的常微分方程求解器解 |
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| 引用本文： | 李世荣,龚云. 功能梯度材料梁自由振动问题的常微分方程求解器解[J]. 兰州理工大学学报, 2009, 35(6) |
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| 作者姓名： | 李世荣 龚云 |
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| 作者单位： | 兰州理工大学,理学院,甘肃,兰州,730050;兰州理工大学,理学院,甘肃,兰州,730050 |
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| 基金项目： | 国家自然科学基金，教育部博士点基金 |
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| 摘 要： | 建立具有连续分布参数的功能梯度材料Euler梁、Timoshenko梁自由振动的动力学方程,以常微分方程求解器为工具,分析计算这两种梁的自振频率;同时讨论Timoshenko梁的自振频率和振型随梁的参数而变化的规律,给出Timoshenko梁的弯曲振动弹性波和剪切振动弹性波的传播速度,分析弯曲和剪切耦合振动的特点和规律.结果表明:常微分方程求解器解和解析解几乎具有同样的精度;自振频率的大小取决于梁在振动时的弹性波的波速;Timoshenko梁在每个频率下的振动均为弯曲和剪切的耦合振动.
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| 关 键 词： | 功能梯度材料 Euler和Timoshenko梁 自由振动分析 弹性波 常微分方程求解器 |
The solutions to free vibration problem of beams with functionally graded materials based on ordinary differential equation solver |
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| LI Shi-rong,GONG Yun. The solutions to free vibration problem of beams with functionally graded materials based on ordinary differential equation solver[J]. Journal of Lanzhou University of Technology, 2009, 35(6) |
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| Authors: | LI Shi-rong GONG Yun |
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| Affiliation: | LI Shi-rong,GONG Yun(School of Science,Lanzhou Univ.of Tech.,Lanzhou 730050,China) |
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| Abstract: | The dynamic equations of free vibration for Euler and Timoshenko beams with functionally graded materials and continuously distributed parameters were developed,respectively.The natural frequencies of the beams were computed and analyzed by employing ordinary differential equation(ODE) solver.The variation of the frequencies and modes of vibration of Tinoshenko beam with the changes of its parameters were discussed.The propagation velocities of elastic waves due to bending and shearing during free vibration... |
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| Keywords: | functionally graded materials Euler and Timoshenko beams free vibration analysis elastic wave ordinary differential equation solver |
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