Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures.

由于双向功能梯度（2D-FG）材料可以满足在消除应力集中，分层和开裂问题以及结构的低成本和轻量化问题的基础上提出的新要求，而不会牺牲刚度和强度，因此这些结构的结构分析变得比以往任何时候都重要。此外，在汽车，军事，航天，生物医学和核能工业中，由2D-FG材料组成的微机电系统的使用正在增加。在这项研究中，基于改进的耦合应力理论，采用横向剪切法向变形梁理论和有限元方法，研究了二维FG多孔微梁的自由振动和屈曲行为。厚度与材料长度尺度参数（MLSP）以及微孔体积分数比，边界条件，长宽比和梯度指数对2D-FG多孔微梁的无量纲基本频率和无量纲临界屈曲载荷的影响为调查。此外，假设材料长度尺度参数可变（VMLSP），则将计算结果与采用恒定MLSP获得的结果进行比较。发现VMLSP增加了2D-FG多孔微梁的刚度，并影响了这些结构的自由振动和屈曲响应。研究了二维多孔玻璃微梁无量纲基频和无量纲临界屈曲载荷的梯度指数。此外，假设材料长度尺度参数可变（VMLSP），则将计算结果与采用恒定MLSP获得的结果进行比较。发现VMLSP增加了2D-FG多孔微梁的刚度，并影响了这些结构的自由振动和屈曲响应。研究了二维多孔玻璃微梁无量纲基频和无量纲临界屈曲载荷的梯度指数。此外，假设材料长度尺度参数可变（VMLSP），则将计算结果与采用恒定MLSP获得的结果进行比较。发现VMLSP增加了2D-FG多孔微梁的刚度，并影响了这些结构的自由振动和屈曲响应。