On the harmonic solution for plate bending: considering the effects of shear deformation and forces in the middle plane

The solution for plate bending under harmonic loads including the geometrical non-linearity effect is presented. The influence of shear deformation and the rotatory inertia in the plate behavior were considered by using the elastodynamic fundamental solution. An additional domain integral was included in the boundary integral equations to consider the geometrical non-linearity effect where in-plane forces were assumed invariant with time and the deflection derivatives dependent of the harmonic solution. An analysis to get the lowest eigenvalue is used to show the relation between maximum values for in-plane forces according to the frequency value. Results obtained when plate rotations were used instead of deflection derivatives in the term related to the geometrical non-linearity effect are discussed and compared to solutions in the literature to show the extension of this strategy.