Free vibration analysis of a spinning functionally graded spherical–cylindrical–conical shell with general boundary conditions in a thermal environment

Abstract

Based on the first-order shear deformation theory (FSDT) for shells, the free vibration of a spinning functionally graded (FG) spherical–cylindrical–conical (SCC) shell with arbitrary boundary conditions subjected to a thermal environment is investigated. The centrifugal forces, the Coriolis forces, and the initial hoop tension caused by spin are all considered in the theoretical modeling. The model is analyzed using the domain decomposition method. The penalty method is used to model the continuity and arbitrary boundary conditions. Validity study is performed by comparing with the results from finite element analyses for special cases. Finally, the effects of the power-law index, the temperature loads, the spinning speed, and the geometrical parameters on the free vibration characteristics, as well as the influences of structural configuration on the critical spinning speed, are investigated. It is found that the configuration of a spinning SCC shell has significant effect on its natural frequency and critical speed under a fixed shell weight. The natural frequencies approximately converge into three values with increases in the circumferential wave number. The FG–SCC shell’s cone angles at which the minimum and maximum natural frequencies occur are not affected by the spinning speed and the power-law index.