FREE VIBRATION ANALYSIS OF ANNULAR FLEXURAL MICRO-PLATES USING C-2 QUADRILATERAL FINITE ELEMENTS

摘要

Using higher continuity C-2 finite elements, vibration of annular flexural micro-plates (FMP) is studied here. The invariant form of the governing equation for micro-plates, with nonlocal effects, based on "modified couple stress theory" is extended for vibration analysis of annular FMP. Nonlocal effects are incorporated in the development of the governing equation by employing the constitutive equation of the strain gradient model which contains only one constant. The resulting sixth-order linear differential equation, cast in polar coordinates, is solved by employing its Galerkin weak form and finite element methodology. The corresponding weak form requires the finite element solution to be at least second-order continuous over the global domain; hence, a new C-2 finite element is formulated to accomplish the required global continuity. Natural frequencies of the annular micro-plates with various boundary conditions are computed using new C-2 finite elements. In order to verify the computational procedure and new element basis, results obtained from the proposed methodology are compared to the closed form solution for simply supported annular plate. Studies of annular FMPs conducted here indicate that incorporation of an internal length parameter can increase the natural frequencies by up to 100% depending on boundary conditions and ratio of the inner and outer radii.