On the critical speed evaluation of arbitrarily oriented rotating doubly-curved shells made of functionally graded materials

The paper presents a general theoretical framework to investigate the dynamic behavior of rotating doubly-curved shell structures made of Functionally Graded Materials (FGMs). A clear advancement of the present formulation is the possibility to apply a rotating speed (angular velocity) about a general axis of the global reference system. It is important to underline that this aspect is innovative with respect to the previous studies proposed in the literature, in which the angular velocity is only applied about the revolution axis the shell. Furthermore, several Higher-order Shear Deformation Theories (HSDTs) are used to investigate the problem at issue. The results of various numerical applications are presented to discuss the effect of the choice of the axis of rotation, as well as the geometric features of the shells, on the dynamic response of the structures. In particular, the analyses are performed to evaluate the critical value of rotating speed, which define the stiffness reduction of the structure. A five-parameter power law is developed to define the variation of the mechanical properties of the FGMs along the thickness of the structures. The accuracy of the current formulation, which includes the effects of both Coriolis and centripetal accelerations, is verified by means of the comparison with the results available in the literature. The solutions are carried out numerically by means of an efficient tool that allows to solve the strong formulation of the governing equations.