Nonlinear vibration of imperfect eccentrically stiffened functionally graded double curved shallow shells resting on elastic foundation using the first order shear deformation theory

•Nonlinear dynamic response and vibration of FGM thick double curved shallow shells.•Using both the first order shear deformation theory and stress function.•FGM shells with imperfection and stiffeners.•FGM shells rest on elastic foundation and subjected to mechanical and damping loads.•Effects of material properties and geometry on dynamic response are discussed.

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of imperfect eccentrically stiffened FGM thick double curved shallow shells on elastic foundation using both the first order shear deformation theory and stress function with full motion equations (not using Volmir's assumptions). The FGM shells are assumed to rest on elastic foundation and subjected to mechanical and damping loads. Numerical results for dynamic response of the FGM shells are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, the material properties, imperfections, the elastic foundations, eccentrically stiffeners and mechanical loads on the nonlinear dynamic response and nonlinear vibration of functionally graded double curved shallow shells. The numerical results in this paper are compared with results reported in other publications.