Effect of voids and cracks on free vibration of FGM plate with parabolic variable thickness

The paper uses the high-order shear deformation theory and the finite element method to analyze the free vibration of rectangular plates. The plate is made of functionally graded materials following an exponential law, with thickness varying parabolically. The Phase-Field theory is applied to describe the state of the material when a crack appears at the center of the plate. To ensure the reliability of the results, the paper compares some results with reputable studies. The analysis of the free vibration of the plate depends on the material composition, crack length, crack inclination angle, plate shape (edge ratio, thickness coefficient) as well as the void coefficient calculated in detail. The numerical results show that the void coefficient, thickness change parameter as well as the crack length greatly affect the oscillation frequency and oscillation form of the plate, while the crack angle has a relatively smaller impact.