An application of a size-dependent model on microplate with elastic medium based on strain gradient elasticity theory

A size-dependent Kirchhoff micro-plate model resting on elastic medium is developed based on the strain gradient elasticity theory. Three material length scale parameters are introduced in the model, and those parameters may effectively capture the size effect. The model can degenerate into the modified couple stress plate model or the classical plate model by setting two (l (0) and l (1)) or all (l (0), l (1) and l (2)) of the material length scale parameters to be zero. Analytical solutions for the static bending, buckling and free vibration problems of a rectangular micro-plate with all edges simply supported are obtained. The results predicted by the present model are compared with those predicted by the degraded models. Influences of the elastic medium on the static bending, buckling, and free vibration are discussed. The results show that the present model can predict prominent size-dependent normalized stiffness, buckling load, and natural frequency with the reduction of structural size, especially when the plate thickness is on the same order of the material length scale parameter. The study may be helpful to guide the design of microplate-based devices resting on elastic medium for a wide range of potential applications.