Free vibrations of small-scale plates with complex shape based on the nonlocal elasticity theory
In the present paper, vibrations of orthotropic nano/microplates of complex shapes are studied. The governing equations are based on the Kirchhoff-Love hypothesis, and the nonlocal theory is used to take into account small-scale effects. The proposed approach uses a variational statement in combination with the Ritz method. A coordinate system is constructed based on the R-functions theory. Plates of various geometric shapes as well as the influence of different types of boundary conditions are studied. The proposed method is applied to the study of an orthotropic plate with two cutouts. The linear frequencies are obtained for a rectangular plate with two cutouts on opposite sides, while the boundary conditions are considered of several types, including simply supported and clamped edges. The small-scale effects for various sizes of cutouts are discussed.
scientific article; zbMATH DE number 7612115