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针对具有复杂弹性支承条件下的欧拉梁,建立其在切向力作用下的运动微分方程.采用广义微分求积法(GDQR)对微分方程在空间上进行离散,获得由动力方程组及边界条件组成的特征值矩阵方程,通过求解特征值矩阵方程来分析梁的稳定性.由计算结果可以发现:剪切系数对临界载荷的影响与梁两端4个支撑弹簧的刚度组合关系密切,当两端各有一个弹簧刚度取无穷大时,剪切系数对临界载荷大小没有影响;随着剪切系数的变化,一端固支、一端弹性支承梁的失稳形式会发生突变.
For the Eulerian beam with complex elastic support, the differential equation of motion is established under the action of tangential force. The differential equation is discretely dispersed by the generalized differential quadrature method (GDQR), and the dynamic equations and the boundary The eigenvalue matrix equation composed of the eigenvalues and eigenvalue matrix equations can be used to analyze the stability of the beam.The results show that the influence of the shear coefficient on the critical load is closely related to the stiffness combination of the four support springs at both ends of the beam, When one end of each spring has infinite stiffness, the shear coefficient has no effect on the critical load. With the change of the shear coefficient, one end is fixed and the instability of one end of the elastic support beam will change suddenly.