Nonlinear dynamic buckling of the imperfect orthotropic E-FGM circular cylindrical shells subjected to the longitudinal constant velocity

In this study, an analytical approach on the nonlinear dynamic buckling of the orthotropic circular cylindrical shells made of exponential law functionally graded material (E-FGM) subjected to the longitudinal constant velocity is investigated with the incorporation of mercurial damping effect. The material properties are assumed to vary gradually in the thickness direction according to an exponential distribution function of the volume fraction of constituent materials. Theoretical formulations are derived based on improved Donnell shell theory (DST) and accounting for von-Kármán strain–displacement relation, initial imperfection and damping effect. By applying Galerkin method and Airy's stress function, the obtained nonlinear differential equations are solved numerically by the fourth-order Runge–Kutta method. The nonlinear dynamic stability of the orthotropic FG cylindrical shell is assessed based on Budiansky–Roth criterion. Additionally, a parametric study is conducted to demonstrate the effects of various velocities, initial imperfections, damping ratios, inhomogeneous parameters on nonlinear dynamic buckling behavior of an imperfect orthotropic FG cylindrical shell. Comparing results with those in other publications validates the proposed method