| 引用本文: | 冯志刚,周建平,李海阳.一维非均匀分布参数系统的渐近传递函数方法.[J].国防科技大学学报,1999,21(2):17-20.[点击复制] |
| Feng Zhigang,Zhou Jianping,Li Haiyang.The Asymptotic Method for One Dimensional Non-uniform Distributed Parameter Systems by Distributed Transfer Function Mcthod[J].Journal of National University of Defense Technology,1999,21(2):17-20[点击复制] |
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| 一维非均匀分布参数系统的渐近传递函数方法 |
| 冯志刚, 周建平, 李海阳 |
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(国防科技大学 航天技术系 湖南 长沙 410073)
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| 摘要: |
| 提出了一维非均匀分布参数系统的一种通用解法: 渐近传递函数方法。对一般的一维非均匀分布参数系统, 引入状态变量将控制方程及边界方程写成状态空间形式。通过定义小参数和摄动方法, 使之变成常系数微分方程, 从而得到问题的摄动解。各阶摄动解均具有规范的形式, 是一以传递函数为积分核的积分形式解析解。文中最后给出了一些数值算例, 验证了方法的有效性。 |
| 关键词: 传递函数, 摄动法, 非均匀分布参数系统 |
| DOI： |
| 投稿日期：1998-06-15 |
| 基金项目:国家自然科学基金、国家教委归国留学人员基金和校预研基金资助 |
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| The Asymptotic Method for One Dimensional Non-uniform Distributed Parameter Systems by Distributed Transfer Function Mcthod |
| Feng Zhigang, Zhou Jianping, Li Haiyang |
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(Department of Aerospace Technology, NUDT, Changsha, 410073)
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| Abstract: |
| Non-uniform beam-like structures have been widely used in engineering structures to achieve an optimal distribution of strength, stiffness and modes of vibration to satisfy design requirements. In this paper, a new asymptotic method for the analysis of these systems is presented. The linear partial differential equation which governs the response of the beam and the inhomogeneous boundary conditions have been put into a state space form. Choosing the small parameterεas a perturbation parameter, the asymptotic solutions are determined by the state space technique. Numerical examples are provided to illustrate the efficiency of the method. |
| Keywords: transfer function, the perturbation method, non-uniform distributed parameter system |
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