Three-dimensional free vibration of functionally graded truncated conical shells subjected to thermal environment

A three-dimensional (3D) free vibration analysis of the functionally graded (FG) truncated conical shells subjected to thermal environment is presented. The material properties are assumed to be temperature-dependent and graded in the radius direction, which can vary according to a simple power law distribution. The initial thermal stresses are obtained accurately by solving the thermoelastic equilibrium equations and by considering the two-dimensional axisymmetric temperature distribution in the shell. The differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to solve the thermal and thermo-mechanical governing equations. For this purpose, a mapping technique is employed to transform the cross section of the shell into the computational domain of DQM. The convergence behavior of the method is numerically demonstrated and comparison studies with the available solutions in the literature are performed. The effects of temperature dependence of material properties, geometrical parameters, material graded index, thermal and mechanical boundary conditions on the frequency parameters of the FG truncated conical shells are carried out.

► 3D free vibration analysis of the functionally graded truncated conical shells is presented.
► Two-dimensional axisymmetric temperature distribution in the shell is assumed.
► The material properties are assumed to be temperature-dependent.
► Initial thermal stresses due to thermal environment are evaluated accurately and included.
► Representing the effects of different parameters on the non-dimensional frequencies.