The natural frequency and mode shape calculation for thin rectangular plate:

intact plate:

single-edge cracked plate:

double-edge cracked plate:

centre cracked plate

Modelling cracks using corner functions:

to be updated

References:

The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method (Yuan and Dickinson, 1992)

Vibrations and stability of a loaded side-cracked rectangular plate via the MLS-Ritz method (Zeng, et al, 2016)

Nonlinear vibration of cracked rectangular Mindlin plate with in-plane preload (Xue, et al, 2020)

Buckling and free vibration of a side-cracked Mindlin plate under axial in-plane load (Xue, et al, 2020)

Free in-plane vibration analysis of rectangular plates with arbitrary elastic boundaries (Lorenzo Dozio, 2010)

The Rayleigh-Ritz method for structural analysis (Ilanko, et al, 2014)