This paper investigates the thermal vibration and buckling of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral plate using the meshless method. Four distributions of the reinforcements along the thickness direction are considered, which are the uniform distributions (UD), FG-V, FG-O and FG-X. The corresponding effective material properties including Young's modulus, mass density, Poisson's ratio and thermal expansion coefficients are estimated by the rule of mixture with the CNT efficiency parameters accounting for the size-dependence. The first-order shear deformation theory (FSDT) with the consideration of thermal effects is employed. Based on Hamilton's principle and the moving least square (MLS) approximation, the discrete governing equations for the vibration of the FG-CNTRC plate are derived. The free vibration of the regular and irregular plates with and without the temperature effect are considered respectively, and the corresponding natural frequencies and mode shapes are obtained by the eigenvalue problem. The stability analysis of the uniaxial and biaxial mechanical and thermal buckling are also conducted subsequently. The effects of the volume fraction, distribution pattern, geometrical characteristics and temperature on the buckling behaviors of the CNTRC quadrilateral plate are discussed in detail.

本文采用无网格方法研究功能梯度碳纳米管增强复合材料（FG-CNTRC）四边形板的热振动和屈曲。考虑沿厚度方向的增强件的四个分布，即均匀分布（UD），FG-V，FG-O和FG-X。相应的有效材料性能包括杨氏模量，质量密度，泊松比和热膨胀系数，是根据混合规则估算的，其中CNT效率参数考虑了尺寸依赖性。采用考虑热效应的一阶剪切变形理论（FSDT）。基于汉密尔顿原理和最小二乘（MLS）逼近，推导了FG-CNTRC板振动的离散控制方程。分别考虑了有和没有温度效应的规则板和不规则板的自由振动，并通过特征值问题获得了相应的固有频率和振型。随后还进行了单轴和双轴机械屈曲和热屈曲的稳定性分析。详细讨论了体积分数，分布模式，几何特征和温度对CNTRC四边形板屈曲行为的影响。