Vibration of cracked rectangular plates including transverse shear deformation and rotary inertia

Abstract

A numerical method based on the Rayleigh method for predicting the natural frequencies of a rectangular plate with a centrally located crack is presented. The effects of transverse shear deformation and rotary inertia are included by applying the dynamic equivalent of the simplified Reissner theory. Numerical results are presented for isotropic and orthotropic rectangular plates. The common notion that the effect of rotary inertia is negligible with respect to the effect of transverse shear deformation is found to be valid only for cracked orthotropic plates. In respect of cracked isotropic plates, the inclusion of rotary inertia reduces the fundamental frequency of a thick isotropic plate with a long crack by an additional amount comparable to the amount caused by the shear deformation alone.