Size-dependent free vibration analysis of Mindlin nano-plates with curvilinear plan-forms by a high order curved hierarchical finite element

摘要

In the present study, Eringen nonlocal theory is employed in Mindlin plate theory to study the free vibration of nano-plates. The hierarchical finite element method based on a curved hierarchical quadrilateral element is developed and applied to free vibration analysis of arbitrary shaped Mindlin nano-plates. Equations of motion for free vibration of arbitrary nano-plate are derived according to the principle of virtual displacements. The convergence and accuracy of the proposed method are demonstrated by comparison with other methods. Finally the effect of aspect ratio, thickness ratio, mode number, and the boundary conditions on the natural frequencies have been studied.