中文摘要：

考虑地基水平摩阻和抗剪能力及梁的剪切变形影响，建立双参数地基Timoshenko深梁的平衡方程，导出微分方程的初参数解和传递矩阵法，利用初参数解建立有限元列式和单元内均布荷载、集中力、集中力偶等非结点荷载的等效公式。当水平摩阻劲度系数为0时，地基退化为传统的双参数地基，当抗剪劲度系数为0时，可进一步退化成Winkler地基，当梁的抗剪劲度无穷大时，Timoshenko梁可退化成Euler梁，因此本模型是一种通用模型。利用传递矩阵法和有限元法分析不同地基模式对在跨中集中力偶作用下两端自由Timoshenko梁的影响、水平摩阻对在集中力、集中力偶和分布荷载共同作用下的一端铰支一端自由阶梯Timoshenko梁的影响。算例结果表明：传递矩阵法结果与有限元结果完全一致，可相互验证其正确性，有限元精度不依赖于单元划分密度，水平摩阻对弹性地基梁有较大影响。

英文摘要：

Considering the shear capacity and horizontal friction of elastic foundation and the shear deformation effect of beam, the equilibrium equation for Timoshenko beam resting on a two-parameter foundation was derived. The initial parameter solution and transfer matrix method were deduced. Using the initial parameter, a finite element formulation and the equivalent nodal forces of the distributed load, concentrated load and concentrated moment were presented. When the horizontal friction rigidity was zero, the foundation model degenerated into the classical two-parameter foundation, when the shear rigidity was zero, Winkler foundation was obtained. If the shear rigidity of beam approached infinity, Timoshenko beam can be converted into Euler beam. The present model was a general model. Using transfer matrix method and finite element method, the influences of different foundation modes on Timoshenko beam with free-free ends under concentrated moment and horizontal friction on stepped Timoshenko beam with hinged-free ends under concentrated load, moment and distributing load were analyzed. Example results show that the transfer matrix method is consist with the finite element method, the accuracy of finite element method does not depend on the mesh density, the horizontal friction may significantly affect elastic foundation beam.