Vibration Analysis of Circular Arch Element Using Curvature. (2008)

• Record Type: Journal Article
• Authors: Saffari, H.; Tabatabaei, R.; Mansouri, S.H.
• Is Part Of: Shock and vibration. Volume 2008(2008)
• Page Start: 481
• Page End: 492
• Publication Date: 2008
• Subjects: Circular arch element -- curvature -- free vibration -- natural frequencies -- membrane-shear locking; Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2008/149393
• Languages: English
• ISSNs: 1070-9622

Abstract

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.