Eventos Anais de eventos
MECSOL 2019
7th International Symposium on Solid Mechanics
Hierarchical methods for free vibration of thin curved beams
Submission Author:
Ramon Macedo Corrêa , PR , Brazil
Co-Authors:
Ramon Macedo Corrêa, Marcos Arndt, ROBERTO Dalledone Machado
Presenter: Ramon Macedo Corrêa
doi://10.26678/ABCM.MECSOL2019.MSL19-0021
Abstract
In this paper the use of hierarchical methods for free vibration of thin curved beams is explored. Two hierarchical approaches using the Generalized Finite Element Method and the Hierarchical Finite Element Method are proposed. Free vibration analyses using these two approaches and the hierarchical Fourier p-element available in literature are performed in order to obtain the natural frequencies of circular rings, modeling one quarter of ring by taking advantage of ring symmetry. Convergence tests of the natural frequencies are performed and the responses of the three methods are compared with analytical solution found in the literature. It is also evaluated the evolution of the mass matrix’s condition number with the increase of the refinement. A second model of a pinned-pinned arch is evaluated to prove the methods efficiency.
Keywords
free vibration, Thin Curved Beams, Hierarchical methods
