Vibration Analysis of Porous Functionally Graded Material Truncated Conical Shells in Axial Motion

In this study, a vibration equation for axially moving truncated conical thin shells made of functionally gradient materials with uniformly and non-uniformly distributed pores has been established based on classical thin shell theory. The free vibration and dynamic response solutions are obtained using the Galerkin method. The effects of axial velocity, half cone angle, ceramic material mass composition, material component index, and internal porosity on the free vibration and dynamic response of mentioned shells were analyzed and discussed. The results show that the increase of axial velocity, half cone angle, and material composition index all decrease the natural frequency of the truncated conical shell but amplify its dynamic response, and the rise of the mass fraction of the ceramic material increases the natural frequency of the truncated conical shell but reduces the dynamic response. The results also demonstrate that compared with non-uniformly distributed pores, the effects of uniformly distributed pores on the shells’ dynamic responses are more evident under axial motion.