Free vibrations analysis of composite and hybrid axisymmetric shells

The free vibration of laminated composite (C) and hybrid axisymmetric shell structures, consisting of a composite laminated material sandwiched between two functionally graded material laminas (F1/C/F2), is analysed in the present work. The numerical solutions are obtained by expanding the variables in Fourier series in the circumferential direction and using conical frustum finite elements in the meridional direction. The implemented finite element is a simple conical frustum with two nodal circles, with ten degrees of freedom per nodal circle. This model requires only a reduced number of finite elements to model the geometry of axisymmetric structures, the integration procedures use one Gauss point, and the through the thickness properties variation in FGM laminas is modelled by a small number of virtual layers, resulting a very high computational efficiency. The inhouse developed code presents very good solutions when compared with results obtained by alternative available models.