Free vibration analysis of cracked plates using peridynamics

In this study, free vibration analysis of cracked plates was performed by using peridynamics. Peridynamics is a new continuum mechanics formulation which is especially suitable for problems including discontinuities such as cracks. A peridynamic Mindlin plate formulation was used and the numerical implementation was done using commercial finite element software, ANSYS. First, the formulation was verified by considering intact and cracked plates and peridynamic solutions were compared against numerical, theoretical and experimental results available in the literature. Once the formulation was verified, the effect of plate thickness, crack size and crack orientation on the natural frequencies were investigated for a centrally cracked plate. It was found that natural frequency values increase as plate thickness increases. On the other hand, increase in crack length decreases the natural frequency values. Moreover, crack orientation also increases natural frequencies for larger cracks. Finally, linear variation of thickness inside the plate causes a tilt of the mode shapes towards the thin side of the plate.