Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler–Pasternak foundation with different boundary conditions under thermal environment

In this paper, the analytical free-vibration analysis of a stiffened functionally graded circular cylindrical shell resting on a Winkler–Pasternak foundation is reported. Various boundary conditions and the thermal effect are considered. Material properties are assumed to be temperature-dependent and vary continuously across the shell’s thickness according to the power law distribution of the volume fraction of constituents. In order to derive the governing equations of the cylindrical shell structure, Hamilton’s principle together with the first-order shear deformation theory and the Lekhnitsky smeared stiffener technique is applied. The natural frequencies of the shell are determined by applying the Galerkin method together with the beam functions for the axial displacement fields. A good agreement between the present results and those available in the literature is observed. In numerical investigations, the influence of temperature field, material volume fraction index, elastic foundation coefficients, boundary conditions, and geometrical ratios on the fundamental natural frequencies of the shell is also given and discussed in detail.