| 陈强,杨国来,王晓锋.移动集中质量作用下Euler-Bernoulli梁的振动频率分析[J].计算力学学报,2012,29(3):340~344,351 |
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| 移动集中质量作用下Euler-Bernoulli梁的振动频率分析 |
| Natural frequency analysis of Euler-Bernoulli beam subjected to moving mass |
| 投稿时间：2010-11-01 修订日期：2011-08-28 |
| DOI：10.7511/jslx20123008 |
| 中文关键词: 移动质量 梁 振动频率 谱元法 Wittrick-Williams算法 |
| 英文关键词:moving mass beam natural frequency spectral element method Wittrick-Williams algorithm |
| 基金项目:国家重点基础研究发展计划(973)(613116)资助项目. |
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| 中文摘要: |
| 研究了移动载荷作用下Euler-Bernoulli梁振动频率的变化规律。首先根据Euler-Bernoulli梁振动的控制方程,引入载荷和位移边界条件,建立梁单元的动力刚度矩阵和形状函数矩阵,然后采用傅里叶变换的思想,建立移动载荷惯性力引起的附加动力刚度矩阵,进而得到系统整体的动力刚度矩阵。通过Wittrick-Williams法进行求解得到移动载荷作用下Euler-Bernoulli梁的振动频率,与有限元法计算结果的比较,验证了此方法的正确性,体现了此方法在精度和计算规模上的优势。根据上述方法,揭示简支梁和悬臂梁振动频率随着移动质量速度与质量的变化规律。 |
| 英文摘要: |
| To analyze the natural frequencies of Euler-Bernoulli beam subjected to moving mass,based on the beam’s governing function,the dynamic stiffness matrix and the shape function matrix of Euler-Bernoulli beam element were deducted by introducing the force and displacement boundary condition.The attached dynamic stiffness matrix which is caused by the moving mass’ inertial force was developed by Furious Transformation.The dynamic stiffness matrix of the whole system was then set up,and the natural frequencies of Euler-Bernoulli beams subjected to moving mass were calculated through Wittrick-Williams algorithm.The method is validated in comparison with FEM results,and is proved of higher precision and smaller computing size.In addition,the rules of simple-supported or cantilever beams’ natural frequencies varying against the velocity,density of moving concentrated mass were brought forth according to this method. |
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