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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

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

Краткое описание

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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