Bi-Hierarchical Finite Element for the Analysis of the Non Axisymetric Free Vibration of Shells of Revolution

Abstract eng:
A new hierarchical finite element is developed to analyze the free vibration of isotropic shells of revolution with linear varying thickness. It is a bi-hierarchical four nodes quadrilateral element with three degrees of freedom (three displacements) by node. The specificity of this element is a double increase of the hierarchical mode number independently according to both axial and radial directions. The advantage is that the solution is accurate for high ratio dimensions as well flattened axisymmetric (plates) shells that slim ones (high cylindrical shells) with different shapes and boundary conditions. The second advantage is the possibility of using only one element to idealize regular shape shells. Through the application of this element to some numerical examples, the comparisons with other studies show clearly that this element gives good results accuracy with simple idealization for axisymmetric and non-axisymmetric shells vibration (thick and thin).

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