A dynamic model for thick elastic plates

In this paper the general equations of motion for thick elastic plates with arbitrary shape are derived by using a variational principle. In addition to the influences of the bending, the transverse shear deformation and the rotatory inertia, the proposed theory also contains the effects of the transverse normal stress and the membrane forces. The equations presented in this paper can be reduced to those deduced by E. Reissner and R. D. Mindlin. Some numerical results are compared with those obtained from the Reissner-Mindlin plate theory and the classical plate theory. It is found that for thick plates there exists a dense region of frequencies and the position of frequencies is shifted, so that the influence of the transverse normal stress must be considered. (C) 1999 Academic Press.