Deriving of statics, dynamics and stability equations for three-layered plates with elastically attached bodies

A set of equations in the normal form is based on the theory of thick shells taking into account the effect of transverse shear deformations. The resolving system of differential equations of motion for multilayered plates has been obtained by use of the Hellinger-Reissner mixed variational principle. The analysis of the dependencies of the plate eigenfrequencies and mode shapes from the body attachment method and resilient members rigidity has been performed.