剪切系数对Timoshenko梁模型影响研究

摘要

Timoshenko首次在梁理论中引入剪切系数用于表征梁的剪应力沿截面的变化，剪切系数对于Timoshenko梁建模至关重要，研究剪切系数对Timoshenko梁模型固有特性的影响。首先采用有限元法建立了动力学模型，给出等截面梁和变截面梁刚度矩阵计算方法，然后研究不同剪切系数对梁频率和振型的影响。结果表明，剪切系数会对模型的频率计算结果带来一定影响，但对振型影响很小，采用第二种剪切系数的模型计算精度更高。%Abstact:Timoshenko was the first tointroduce a shear coefficient to account for the variation of the shear stress along the cross-section, the shear coefficient was important to Timoshenko Beam. The effects of shear coefficients on the inherent characteristics of Timoshenko beam were studied. First, the dynamic model was established using FEM, the calculation methods of stiffness matrices were proposed for uniform beam and non-uniform beam, and then the influence of different coefficients on the frequency and mode shape of beam was discussed. The results show that shear coefficients bring about some influence on frequencies, but have little effect on mode shape; the precision of the model using the second shear coefficient is higher.