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假定纵向摩擦力与梁底面的纵向位移成正比,引入广义剪力,得到广义Winkler型地基上Timoshenko梁的位移型平衡方程。将位移及荷载展开为带附加项的Fourier级数,利用平衡方程和边界条件对弹性地基梁的一般弯曲进行分析。该解答退化后可用来研究传统的Winkler地基上Bernoulli-Euler梁的弯曲问题。分析表明,纵向摩擦力对梁的位移和内力均有影响。梁的最大挠度、转角、弯矩及剪力随着地基纵向摩擦力的增大而减小,而梁的轴向位移和轴力则随着地基纵向摩擦力的增大而增大。
It is assumed that the longitudinal friction is proportional to the longitudinal displacement of the bottom of the beam, and the generalized shear force is introduced to obtain the displacement equilibrium equation of the Timoshenko beam on a generalized Winkler foundation. The displacements and loads are expanded into Fourier series with additional terms, and the general bending of the elastic foundation beam is analyzed by the balance equation and the boundary conditions. This solution can be used to study the bending of the Bernoulli-Euler beam on the traditional Winkler foundation after degeneration. The analysis shows that the longitudinal friction affects the displacement and internal force of the beam. The maximum deflection, corner, moment and shear of the beam decrease with the longitudinal friction of the foundation, while the axial displacement and axial force of the beam increase with the increase of the longitudinal friction of the foundation.