| Bernoulli-Euler梁横向振动固有频率的轴力影响系数 |
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| 引用本文： | 张广芸,张宏生,陆念力.Bernoulli-Euler梁横向振动固有频率的轴力影响系数[J].工程力学,2011(10). |
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| 作者姓名： | 张广芸 张宏生 陆念力 |
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| 作者单位： | 哈尔滨工业大学机电工程学院; |
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| 基金项目： | 国家科技支撑计划项目(2006BAJ12B03-2) |
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| 摘 要： | 给出了考虑轴力对于Bernoulli-Euler梁横向振动固有频率影响系数的高精度表达式。与动力刚度法推导等截面梁自由振动分析的动态刚度阵不同,首先获得承受常轴力的Bernoulli-Euler梁横向自由振动微分方程的通解,并通过位移边界条件消去待定常数,得到精确形函数;使用有限元方法,建立了使用精确形函数表达等截面Bernoulli-Euler梁动态刚度阵的微分格式,该微分格式精确刚度阵与动力刚度法得到的刚度阵完全一致。仿照Timoshenko对压弯梁静态挠度表达中取用轴力影响因子的方法,提出了Bernoulli-Euler梁横向振动固有频率的轴力影响系数表达式,结合Wittrick-Williams算法和动态刚度阵证明了当轴力在±0.5倍第1阶欧拉临界力之间变化时,轴力影响系数表达式最大误差不超过2%,且随固有频率阶次的提高,误差越来越小。
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| 关 键 词： | 有限单元法 精确形函数 自由振动 Bernoulli-Euler梁 轴力影响系数 |
THE AXIAL LOAD INFLUENCE COEENFFICIT OF NATURAL FREQUENCIES FOR LATERAL VIBRATION OF A BERNOULLI-EULER BEAM |
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| ZHANG Guang-yun,ZHANG Hong-sheng,LU Nian-li.THE AXIAL LOAD INFLUENCE COEENFFICIT OF NATURAL FREQUENCIES FOR LATERAL VIBRATION OF A BERNOULLI-EULER BEAM[J].Engineering Mechanics,2011(10). |
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| Authors: | ZHANG Guang-yun ZHANG Hong-sheng LU Nian-li |
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| Affiliation: | ZHANG Guang-yun,ZHANG Hong-sheng,LU Nian-li(School of Mechatronics Engineering,Harbin Institute of Technology,Harbin 150001,China) |
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| Abstract: | A high precision formula is proposed in order to consider the influence coefficient of natural frequencies for the lateral vibration of a Bernoulli-Euler beam subjected to axial loads.It is different from the dynamic stiffness matrix obtained by dynamic stiffness method for the free vibration of the uniform beam.According to the governing differential equation for the lateral vibration of a Bernoulli-Euler beam subjected to a constant axial load,the general solution is obtained.The exact shape function can ... |
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| Keywords: | finite element method exact shape function free vibration Bernoulli-Euler beam axial load influence coefficient |
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