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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2015012014
pages 311-319

FREE VIBRATION ANALYSIS OF ANNULAR FLEXURAL MICRO-PLATES USING C2 QUADRILATERAL FINITE ELEMENTS

Ali R. Ahmadi
Kerman Graduate University of Technology, Kerman, IRAN

ABSTRACT

Using higher continuity C2 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 C2 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 C2 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.


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