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Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness

This paper presents a numerical solution for vibration analysis of cantilevered non-uniform trapezoidal thick plates. Based on the first shear deformation theory, kinetic and strain energies of the plate are derived and using Hamilton's principle, governing equations and boundary conditions are derived. | Nội dung Text Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness Engineering Solid Mechanics 2017 71-92 Contents lists available at GrowingScience Engineering Solid Mechanics homepage www.GrowingScience.com esm Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness Keivan Torabi and Hassan Afshari Department of Solid Mechanics Faculty of Mechanical Engineering University of Kashan Kashan Iran A R T I C L EI N F O ABSTRACT Article history This paper presents a numerical solution for vibration analysis of cantilevered non-uniform Received 6 March 2016 trapezoidal thick plates. Based on the first shear deformation theory kinetic and strain energies Accepted 3 August 2016 of the plate are derived and using Hamilton s principle governing equations and boundary Available online conditions are derived. A transformation of coordinates is used to convert the equations and 3 August 2016 Keywords boundary conditions from the original coordinates into a new computational coordinates. Using Trapezoidal plate Differential quadrature method DQM natural frequencies and corresponding modes are Moderately thick plate derived numerically. Convergence and accuracy of the proposed solution are confirmed using Variable thickness results presented by other authors and also results obtained based on the finite element method Differential quadrature method using ANSYS software. Finally as the case studies two cases for variation of thickness are considered and the effects of angles aspect ratio and thickness of the plate on the natural frequencies are studied. It is concluded that two angles of the trapezoid have opposite effect on the natural frequencies. Also it is shown that all frequencies rise as value of thickness increases or value of the aspect ratio of the plate decreases. The most advantage of the proposed solution is its applicability for plates with variable thickness. 2017 Growing Science .