| 一类非等截面杆的纵向自由振动 |
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| 引用本文： | 郭树起,杨绍普.一类非等截面杆的纵向自由振动[J].石家庄铁道学院学报,2010,23(2):59-63. |
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| 作者姓名： | 郭树起 杨绍普 |
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| 作者单位： | 郭树起(石家庄铁道大学,工程力学系,河北,石家庄,050043);杨绍普(石家庄铁道大学,机械工程学院,河北,石家庄,050043) |
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| 基金项目： | 国家自然科学基金资助 |
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| 摘 要： | 研究一类变截面杆，其横截面积呈指数函数变化。经适当变换后，杆的纵向自由振动方程转换为退化的超几何方程，其解可以用Kummer函数来表示。得到了三种简单边界条件下的频率方程和振型函数。频率方程一般是超越方程，需要数值求解其固有频率。在特殊情形下。可以求得各阶固有频率。
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| 关 键 词： | 变截面杆 纵向振动 自由振动 Kummer函数 超几何方程 |
Free Axial Vibrations of a Non-uniform Rod |
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| Guo Shuqi,Yang Shaopu.Free Axial Vibrations of a Non-uniform Rod[J].Journal of Shijiazhuang Railway Institute,2010,23(2):59-63. |
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| Authors: | Guo Shuqi Yang Shaopu |
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| Institution: | 1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China; 2. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China) |
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| Abstract: | In this paper, the free axial vibrations of a rod with variable cross section area of the cross section of the rod varies exponentially along the axes of the rod. In terms are investigated. The of the proposed transformation, the governing equations of the free vibration are transformed as degenerated hyper-geometry equations, the solutions of which can be expressed by Kummer functions. The frequency equations and mode functions are obtained under three kinds of boundary conditions. Since the frequency equations are transcendental equations, the natural frequencies are solved with a numeric method. For some special cases, the explicit expressions of natural frequencies can be obtained. |
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| Keywords: | rod with variable cross section axial vibration free vibrations Kummer functions hyper-geometry equation |
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