中文摘要：

基于二维弹性理论，研究双参数弹性地基上功能梯度材料梁的自由振动问题．考虑材料属性沿厚度方向呈梯度变化，获得双参数弹性地基上功能梯度材料梁的自由振动控制微分方程，然后运用微分求积法（测）数值求解梁在两端筒支边界条件下自由振动的无量纲固有频率，并将得到结果与现有的文献作了比较，证明微分求积法对求解该问题的有效性．考虑不同参数变化对于梁自由振动频率的影响．结果表明，材料梯度指数和地基模量参数对功能梯度材料梁的无量纲自振频率均有影响．

英文摘要：

Based on the two-dimensional elastic theory, free vibration of functionally graded beams resting on a two-parameter elastic foundation was investigated. Considering the material properties to be graded in the thickness direction, the free vibration governing differential equations for the functionally graded beams on a two-parameter elastic foundation were derived. By using the differential quadrature method （DQM）, the free vibration dimensionless natural frequency parameters of the FGM beams with simply supported boundary condition at two sides were calculated. The formulations are validated to solve the problem using differential quadrature method by comparing the results with those available literatures. Finally, effects of different parameters on the free vibration frequencies of the FGM beams were presented. The results showed that the power law indexes and the foundation moduli parameters affect on dimensionless natural frequencies of functionally graded beams.