Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments

• Nonlinear dynamic response and vibration of the Sigmoid FGM shell.
• Used the third order shear deformation shell theory.
• The shell is surrounded on elastic foundations.
• The S-FGM shell is subjected to mechanical, damping loads and temperature.

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of imperfect functionally graded materials (S-FGM) thick circular cylindrical shells surrounded on elastic foundation using the third order shear deformation shell theory. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents with metal–ceramic–metal layers. The S-FGM shells are subjected to mechanical, damping and thermal loads. The Galerkin method and fourth-order Runge–Kutta method are used to calculate natural frequencies, nonlinear frequency–amplitude relation and dynamic response of the shells. In numerical results, the effects of geometrical parameters, the material properties, imperfections, the elastic foundations and mechanical loads on the nonlinear dynamic response and nonlinear vibration of the shells are investigated. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature.