The effect of cracks and thermal environment on free vibration of FGM plates

The free vibration parameters of cracked functionally graded material (FGM) plates with nonlinear varying thickness according to the symmetric parabola function under temperature is studied in this paper. The temperature transfers through the thickness of the FGM plate and material properties of the plate are distributed power law in the thickness direction and depend on the temperature. The formulas were developed based on Shi's third-order shear deformation theory and the phase field theory in destructive mechanics. The results of the present approach are compared with the existing literature for the validation. The free vibration frequencies of the plate are calculated depending on various parameters such as crack length, crack angle, plate length ratio, temperature, volume fraction index and boundary conditions. In addition, the effect of plate edges and symmetrical parabolic thickness shapes on the natural frequencies of FGM plates are also studied.