基于Eringen非局部线弹性理论，采用n阶广义梁理论(GBT)，应用改进型广义微分求积(MGDQ)法数值研究了初始轴向机械力及热载荷共同作用下功能梯度材料(FGM)纳米梁的耦合振动及耦合屈曲特性。考虑了材料性质的温度相关性，且温度沿梁的厚度方向按不同类型稳态分布，采用Voigt混合幂率模型表征FGM纳米梁的材料属性。在Hamilton体系下统一建立描述结构耦合振动及屈曲问题力学模型的控制微分方程。通过引入梁边界条件控制参数，实施了3种典型边界FGM纳米梁耦合振动响应MGDQ法求解的MATLAB统一化编程。基于屈曲与振动这两类静动态响应之间的二元耦联性，通过编写相应循环子程序用来获得屈曲静态响应。与已有研究结果对比表明：该分析方法切实可行、行之有效，极大地提高了计算效率。最后，分析了梁理论、边界条件、尺度效应非局部参数、初始轴向机械力、温度分布、升温、热-机耦合效应、材料组分梯度指标、跨厚比等诸多参数对FGM纳米梁振动及屈曲特性的影响。

Based on Eringen’s nonlocal linear elastic theory and n-th order generalized beam theory (GBT), the coupled vibration and buckling characteristics of functionally graded material (FGM) nanobeams subjected to thermal-mechanical loads were investigated by using a modified generalized differential quadrature (MGDQ) method.The material properties were temperature-dependent according to the Voigt mixture power-law model and various types of temperature distributions were assumed to be steady along the thickness direction of the structure.The governing differential equations for the coupled vibration and buckling of the system were derived unifiedly in accordance with the Hamilton’s principle.By introducing control parameters for three different kinds of boundary conditions, the MGDQ method was  used to solve the coupled vibration response of the structure with the MATLAB procedure.A loop subprogram was also written to obtain the static responses based on the duality between the vibration and buckling responses of FGM nanobeams.The MGDQ method presented was validated to be available and highly efficient by comparison with those of available results in the literature.Finally, the effects of various beam theories, boundary conditions, nonlocal scale parameters, initial axial mechanical loads, various types of temperature distributions, temperature rises, thermal-mechanical loads, material graded index and slenderness ratios on the vibration and buckling characteristics of FGM nanobeams were studied.