梁端约束条件和梗腋对箱梁弯曲简谐振动的影响

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (23) : 21-28.

论文

张玉元，张元海，张慧，余剑搏

作者信息 +

Effects of beam end constraint condition and corner haunch on bending simple harmonic vibration of box girder

ZHANG Yuyuan,ZHANG Yuanhai,ZHANG Hui,YU Jianbo

Author information +

文章历史 +

摘要

为了分析梁端约束条件和梗腋对箱梁弯曲谐响应的影响，本文以剪力滞效应引起的附加挠度为广义位移，并计入其对体系总动能的影响，运用Hamilton原理建立了考虑剪切剪力滞效应影响的箱梁弯曲简谐振动变分解析解，引入反映箱梁动力特性的截面应力及挠度放大系数，详细分析了梁端约束条件和梗腋对箱梁弯曲谐响应的影响。算例分析表明：不同梁端约束条件和梗腋影响的箱梁谐响应解析解与有限元数值解吻合良好；梁端约束条件越强，附加挠度及翘曲正应力在初等梁计算结果中的占比越大，截面应力及挠度放大系数越小；剪切效应对谐响应的影响大于剪力滞效应，且其差值比随振动频率的增大而增大；梗腋对初等梁谐响应的削弱影响较大，而对剪切剪力滞效应引起的附加挠度、翘曲正应力及放大系数的影响较小，分析梗腋对箱梁弯曲谐响应影响时，可按初等梁振动理论进行计算。

Abstract

In order to analyze the influence of end restraint condition and corner haunch on the bending harmonic response of box girder, the additional deflection caused by shear lag was selected as the generalized displacement in this paper, and its influence on the total kinetic energy of the system was taken into account. The variational analytical solution of bending simple harmonic vibration of box girder considering the shear deformation and shear lag was established by using the Hamilton principle. The stress and deflection amplification factor reflecting dynamic characteristics of box girder were introduced, the influence of end restraint condition and corner haunch on the bending harmonic response of box girder were analyzed in detail. The example analysis shows that the analytical solution of harmonic response of box girder with different end restraint condition and the influence of corner haunch are in good agreement with the finite element numerical solution. The stronger the end restraint condition, the larger the proportion of additional deflection and warping normal stress in the results of elementary beams, and the smaller the amplification factor of stress and deflection. The influence of shear deformation on harmonic response is greater than shear lag effect, and its difference ratio increases with the increase of vibration frequency. The corner haunch has a great influence on the weakening of the harmonic response of the elementary beam, but has little effect on the additional deflection, warping normal stress and amplification factor caused by the shear deformation and shear lag. When analyzing the influence of corner haunch on the bending harmonic response of box girder, it can be calculated according to the elementary beam vibration theory.

导出引用

张玉元，张元海，张慧，余剑搏. 梁端约束条件和梗腋对箱梁弯曲简谐振动的影响[J]. 振动与冲击, 2023, 42(23): 21-28

ZHANG Yuyuan,ZHANG Yuanhai,ZHANG Hui,YU Jianbo. Effects of beam end constraint condition and corner haunch on bending simple harmonic vibration of box girder[J]. Journal of Vibration and Shock, 2023, 42(23): 21-28

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