赵翔, 周扬, 邵永波, 刘波, 周仁. 基于Green函数法的Timoshenko曲梁强迫振动分析[J]. 工程力学, 2020, 37(11): 12-27. DOI: 10.6052/j.issn.1000-4750.2019.11.0708
引用本文: 赵翔, 周扬, 邵永波, 刘波, 周仁. 基于Green函数法的Timoshenko曲梁强迫振动分析[J]. 工程力学, 2020, 37(11): 12-27. DOI: 10.6052/j.issn.1000-4750.2019.11.0708
ZHAO Xiang, ZHOU Yang, SHAO Yong-bo, LIU Bo, ZHOU Ren. ANALYTICAL SOLUTIONS FOR FORCED VIBRATIONS OF TIMOSHENKO CURVED BEAM BY MEANS OF GREEN’S FUNCTIONS[J]. Engineering Mechanics, 2020, 37(11): 12-27. DOI: 10.6052/j.issn.1000-4750.2019.11.0708
Citation: ZHAO Xiang, ZHOU Yang, SHAO Yong-bo, LIU Bo, ZHOU Ren. ANALYTICAL SOLUTIONS FOR FORCED VIBRATIONS OF TIMOSHENKO CURVED BEAM BY MEANS OF GREEN’S FUNCTIONS[J]. Engineering Mechanics, 2020, 37(11): 12-27. DOI: 10.6052/j.issn.1000-4750.2019.11.0708

基于Green函数法的Timoshenko曲梁强迫振动分析

ANALYTICAL SOLUTIONS FOR FORCED VIBRATIONS OF TIMOSHENKO CURVED BEAM BY MEANS OF GREEN’S FUNCTIONS

  • 摘要: 该文运用Green函数法求解了Timoshenko曲梁在强迫振动下的解析解,通过分析曲梁截面的力学平衡,建立了Timoshenko曲梁的振动方程。依次采用分离变量法和Laplace变换法,对不同边界的Timoshenko曲梁求解出了相应的Green函数。并且通过引入两个特征参数来考虑阻尼对强迫振动的影响。数值计算中,验证了该解析解的有效性,并对其中涉及的各种重要物理参数的影响进行了研究。研究结果表明:通过将半径R设置为无穷大,可以简化为Timoshenko直梁振动模型,在此基础上,将剪切修正因子κ设置为无穷大,可以退化为Prescott直梁振动模型,最后再把转动惯量γ设置为0,可退化为Euler-Bernoulli直梁振动模型。该文给出的数值结果验证了所得解的有效性。

     

    Abstract: This paper derives analytical solutions for the forced vibrations of Timoshenko curved beams and establishes the vibration equation of Timoshenko curved beams by analyzing the equilibrium equation for the intersection of curved beams. Green’s functions of Timoshenko curved beams are solved for different boundary conditions using the separation of variables and Laplace transform. Two characteristic parameters are introduced to measure damping effects on beam vibrations. Numerical calculations are conducted to validate analytical solutions, and the effects of various related physical parameters are investigated. The results show that by setting the radius R to infinity, it can be simplified to the Timoshenko straight beam vibration model, and on this basis, if the shear correction factor κ is set to infinity, it can be reduced to the Prescott straight beam vibration model. Finally, the moment of inertia γ is set to 0, which can be reduced to the Bernoulli-Euler straight beam vibration model. Numerical calculations are performed to validate the solutions.

     

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