In this paper, Shi's high-order shear deformation theory (HSDT) is introduced to compute the free vibration of the cracked functionally graded material (FGM) plates according to the power law resting on Pasternak elastic foundations. The rectangular plate has a linearly variable thickness and has a crack in the center. The phase field theory and finite element method are used to study the vibration frequency of plates depending on the exponent of the material as well as the parameters of the elastic foundation. Several numerical results have been compared with the ones available in the literature. Next, the paper investigates the effect of length, angle of crack, ratio of plate thickness to the free vibration of plates.

本文采用Shi的高阶剪切变形理论（HSDT），根据Pasternak弹性地基上的幂定律，计算开裂的功能梯度材料（FGM）板的自由振动。矩形板具有线性可变的厚度并且在中心具有裂纹。根据材料的指数以及弹性地基的参数，利用相场理论和有限元方法研究板的振动频率。已将几个数值结果与文献中提供的数值结果进行了比较。接下来，研究了长度，裂纹角度，板厚比对板自由振动的影响。