Abstract
An annular sector solid hierarchical finite element is presented and applied to three-dimensional free vibration analysis of annular sector plates. The element's displacements are expressed in terms of a fixed number of linear polynomial shape functions plus a variable number of shape functions which are forms of the shifted Legendre orthogonal polynomial. The linear polynomial shape functions are used to describe the element's nodal displacements and the higher order shape functions are used to provide additional freedom to the edges, faces, and interior of the element. Results of frequency calculations are found for annular sector plates with two straight edges simply supported like a diaphragm condition and comparisons are made with those obtained by the finite prism method. The manner of convergence of the solution as a function of the numbers of hierarchical modes is also investigated. Furthermore, contributions to original three-dimensional frequencies are made for annular sector plates with other boundary conditions along the two straight edges.
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