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Shock and Vibration
Volume 15, Issue 5, Pages 481-492
http://dx.doi.org/10.1155/2008/149393

Vibration Analysis of Circular Arch Element Using Curvature

H. Saffari,1 R. Tabatabaei,1 and S.H. Mansouri2

1Civil Engineering Department, University of Kerman, Kerman, Iran
2Mechanical Engineering Department, University of Kerman, Kerman, Iran

Received 20 July 2006; Revised 22 February 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, a finite element technique was used to determine the natural frequencies, and the mode shapes of a circular arch element was based on the curvature, which can fully represent the bending energy and by the equilibrium equations, the shear and axial strain energy were incorporated into the formulation. The treatment of general boundary conditions dose need a consideration when the element is incorporated by the curvature-based formula. This can be obtained by the introduction of a transformation matrix between nodal curvatures and nodal displacements. The equation of the motion for the element was obtained by the Lagrangian equation. Four examples are presented in order to verify the element formulation and its analytical capability.