Analytical solution approach for nonlinear vibration of shear deformable imperfect FG-GPLR porous nanocomposite cylindrical shells

This study presents an analytical solution approach to examine the nonlinear vibration of geometrically imperfect functionally graded porous circular cylindrical shells reinforced with graphene platelets (GPL) surrounded on an elastic foundation. First-order shear deformation theory is employed to formulate the considered problem. Four porosity distributions and four GPLs dispersion patterns are considered which vary through the thickness direction. The effective mechanical properties of considered functionally graded graphene platelet-reinforced porous nanocomposites are characterized via a micromechanical model. Governing equations are derived by Hamilton's principle and then were transformed into a set of ordinary differential equations using the Galerkin method. Afterward, the nonlinear frequency response curves are obtained with the use of the method of multiple scales. Numerical results are provided to explore the effect of parameters such as initial imperfection, geometry, porous distribution, porosity coefficient, and GPLs' scheme and weight fraction on the nonlinear frequency-response curve.