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- Vibrations of functionally graded material axisymmetric shellsPublication . Simões Moita, José Mateus; Araújo, Aurélio L.; Franco Correia, Victor; Soares, Cristóvão M. MotaThe free-vibration analysis of functionally graded materials (FGM) axisymmetric plate-shell type structures are presented in this work. A numerical solution is obtained by expanding the variables in Fourier series in the cir-cumferential direction and using conical frustum finite elements in the meridional direction. The finite element model, having two nodal circles and ten degrees of freedom per node, is based in the Kirchhoff-Love theory that include the transverse shear deformations by introducing a penalty function, and using one Gauss point inte-gration scheme which gave excellent results for both thin and thick axisymmetric plate/shells structures. The reduced number of finite elements, which are required to model even complex structures, combined with the use of a small number of discrete layers to model the continuous variation of the mechanical properties through the thickness of the structure, result in an extremely low computational time required for FGM applications. An in-house program has been developed, and applications in a variety of axysimetric shells are solved, including circular plates. The solutions obtained are discussed and compared with solutions obtained by alternative models.