考虑界面摩阻效应的弹性地基梁微分算子级数解法

假定地基为具有水平和竖向反力的弹性支撑体，考虑弹性地基梁的纵横向耦合变形，根据弹性力学基本原理，从梁体微段分析出发，结合小变形条件下梁体几何方程和线弹性本构关系，导得考虑摩阻效应时关于竖向位移和水平位移的基本微分方程组，并在此基础上利用微分算子级数法对微分方程组进行求解，导得了考虑纵横向耦合变形和界面摩阻效应时地基梁竖向挠度和水平相对位移计算公式。最后对某一地基梁实例进行了计算分析，并对摩阻效应进行了讨论。其结果表明，微分算子级数法解答能有效地考虑地基梁纵横向耦合变形特征和界面摩阻效应。

Differentiator series calculation method for beams on elastic foundation considering interface frictional effect

The subgrade is assumed to be hinge-spring system with horizontal and vertical reactions and the vertical-horizontal coupling distortion of beam on elastic foundation is considered. Based on the basic principles of Elasticity and analysis of micro-segment of beam, the basic differential equation about vertical displacement and horizontal one is deduced with frictional effect considered on the Combination of geometric equation and linear-elastic constitutive equation of beam under little deformation. Then on the basis of that, the differential equation is solved by means of differentiator series calculation method and the calculation formulas for vertical deflection and horizontal relative displacement are deduced considering vertical-horizontal coupling distortion and interface frictional effect. Lastly a example for beam on elastic foundation is analyzed and frictional resistance is discussed. The results show that the vertical-horizontal coupling distortion and effect of horizontal frictional resistance can be considered effectively in the differentiator series calculation method.