Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment

Analytical solutions for the nonlinear vibration of imperfect functionally graded nanocomposite (FG-CNTRC) double curved shallow shells on elastic foundations subjected to mechanical load in thermal environments are introduced in this paper. The double curved shallow shells are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction according to the different types of linear functions. Motion and compatibility equations are derived using Reddy's higher order shear deformation shell theory and taking into account the effects of initial geometrical imperfection and temperature- dependent properties. The deflection- time curve and the natural frequency are determined by using Galerkin method and fourth- order Runge- Kutta method. The effects geometrical parameters, elastic foundations, initial imperfection, temperature increment, mechanical loads and nanotube volume fraction on the nonlinear thermal vibration of the nanocomposite double curved shallow shells are discussed in numerical results. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.