The Effect of Cracks on the Free Vibration of a Plate with Parabolic Thickness

This paper uses first-order shear deformation theory and the finite element method to analyze the vibrations of rectangular plates with one or more cracks. The study investigated the influence of cracks (length, angle of inclination), the number of cracks, and the ratio of plate thickness to the natural vibration frequency of the plate, using phase field simulation. Plate thickness varies nonlinearly with the parabolic function. The results of the proposed method were compared with reputable studies to verify its reliability. In addition, some pictures of the characteristic vibration patterns of the plate with varying thickness are presented when cracks appear.