Abstract
<jats:p>In the present paper a moment-membrane linear dynamic theory of plane stress state and transverse bending of elastic plates is presented as continual theories of the deformation behavior of a graphene sheet. In solutions of these problems of a graphene sheet a finite element method is developed, based on the variational formulation of the corresponding problems. The theory and basic relations of a rectangular finite element are presented for calculating natural vibrations of a graphene sheet (rectangular plate). Based on this theory the problem of natural vibrations of transverse bending of a graphene sheet is specifically considered. The questions of practical convergence of the solution and assessment of the accuracy of the finite element method are discussed.</jats:p>