Strain Gradient Theory Based Dynamic Mindlin-Reissner and Kirchhoff Micro-Plates with Microstructural and Micro-Inertial Effects

In this study, a dynamic Mindlin–Reissner-type plate is developed based on simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations motion and the corresponding boundary conditions are derived using general virtual work variational principle. presented model contains, apart from two classical Lame constants, one additional microstructure material parameter g for static case micro-inertia h case. formal reduction to Kirchhoff-type also presented. Upon diminishing parameters h, Mindlin–Reissner Kirchhoff theories derived. Three points distinguish present other similar published in literature. First, plane stress assumption, fundamental development theories, expressed by vanishing z-component generalized true traction vector not merely zz-component Cauchy tensor. Second, terms included expression kinetic energy model. Finally, detailed structure non-classical both micro-plates. An example simply supported rectangular used illustrate proposed compare it with results numerical reveal significance strain effect bending free vibration response micro-plate, when thickness at micron-scale; comparison plates, deflections, rotations, shear-thickness frequencies smaller, while flexural frequency higher. It observed that should be ignored estimating micro-plates, primarily thick micron scale (strain effect).