Vibration analysis of circular arch element using curvature

Article type: Research Article

Authors: Saffari, H. | Tabatabaei, R. | Mansouri, S.H.

Affiliations: Civil Engineering Department, University of Kerman, Kerman, Iran | Mechanical Engineering Department, University of Kerman, Kerman, Iran

Note: [] Corresponding author. Tel.: +98 9133429226; Fax.: +98 341 3211497; E-mail: [email protected]

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.

Keywords: Circular arch element, curvature, free vibration, natural frequencies, membrane-shear locking

Journal: Shock and Vibration, vol. 15, no. 5, pp. 481-492, 2008