| 基于Bessel和Meijer-G函数的楔形和锥形悬臂梁振动分析 |
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| 引用本文： | 周坤涛,杨涛,葛根,郝淑英,张琪昌. 基于Bessel和Meijer-G函数的楔形和锥形悬臂梁振动分析[J]. 振动与冲击, 2022, 0(4): 253-261 |
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| 作者姓名： | 周坤涛 杨涛 葛根 郝淑英 张琪昌 |
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| 作者单位： | 天津工业大学机械工程学院;天津理工大学工程训练中心;天津理工大学机械工程学院;天津大学机械工程学院 |
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| 基金项目： | 国家自然科学基金(12072234,11872044,12072233);天津市自然科学基金(20JCYBJC00510)。 |
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| 摘 要： | 基于欧拉-伯努利梁理论,利用Lagrange法建立了楔形和锥形截面梁在外激作用下的非线性微分方程.提出了一种基于Bessel函数和Meijer-G函数线性组合的无需迭代及近似截断的振型函数,且该振型函数不依赖于楔形和锥形变截面梁的弯曲振动的运动方程是否为标准的Bessel形式,该方法能快速求解线性基频和模态函数.随后将...
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| 关 键 词： | 欧拉-伯努利梁 Lagrange法 Bessel函数 Meijer-G函数 非线性振动 |
Vibration analysis of wedge and cone cantilever beams based on Bessel and Meijer-G functions |
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| ZHOU Kuntao,YANG Tao,GE Gen,HAO Shuying,ZHANG Qichang. Vibration analysis of wedge and cone cantilever beams based on Bessel and Meijer-G functions[J]. Journal of Vibration and Shock, 2022, 0(4): 253-261 |
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| Authors: | ZHOU Kuntao YANG Tao GE Gen HAO Shuying ZHANG Qichang |
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| Affiliation: | (School of Mechanical Engineering,Tiangong University,Tianjin 300387,China;Engineering Training Center,Tianjin University of Technology,Tianjin 300384,China;School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China;School of Mechanical Engineering,Tianjin University,Tianjin 300072,China) |
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| Abstract: | In this paper,a nonlinear differential equation model of wedge and cone cantilever beams under external excitation was investigated by the Lagrange method based on the Euler-Bernoulli beam theory.A new type of modal function without iteration and approximate truncation was proposed based on the linear combination of Bessel and Meijer-G functions and it does not depend on whether the equation of motion of the wedge and cone beam in flexural vibration is a standard Bessel form,which can quickly solve linear fundamental frequency and mode shape function.Subsequently,by substituting the modal function obtained in this paper into the governing equation of the vibrating tapered cantilever,the curvature nonlinear coefficient and the inertia nonlinear coefficient were obtained.Finally,the amplitude-frequency response of the nonlinear primary resonance under a given vibration mode was determined using the method of multiple scales.The results show that the linear fundamental frequency and nonlinear amplitude-frequency response curves obtained by the method in this paper are highly consistent with the results of existing literature. |
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| Keywords: | Euler-Bernoulli beam Lagrange method Bessel function Meijer-G function nonlinear vibration |
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