Free vibration of functionally graded truncated conical shells under internal pressure

The influence of internal pressure on the free vibration behavior of functionally graded (FG) truncated conical shells are investigated based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses are obtained by solving the static equilibrium equations. Using Hamilton’s principle and by including the influences of initial stresses, the free vibration equations of motion around this equilibrium state together with the related boundary conditions are derived. The material properties are assumed to be graded in the thickness direction. The differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to discretize the governing equations and the related boundary conditions. The convergence behavior of the method is numerically investigated and its accuracy is demonstrated by comparing the results in the limit cases with existing solutions in literature. Finally, the effects of internal pressure together with the material property graded index, the semi-vertex angle and the other geometrical parameters on the frequency parameters of the FG truncated conical shells subjected to different boundary conditions are studied.