The dynamic stability of orthotropic cylindrical shells with non-homogenous material properties under axial compressive load varying as a parabolic function of time

In this study, the dynamic stability problem of a cylindrical shell composed of non-homogeneous orthotropic materials with Young's moduli and density varying continuously in the thickness direction under the effect of an axial compressive load varying with a parabolic function of time is considered. At first, the fundamental relations and the modified Donnell type dynamic stability equations of a non-homogeneous orthotropic cylindrical shell are set up. Applying the Galerkin method, first, and then the Ritz-type variational method, the closed-form solutions have been derived for the dynamic critical axial load and dynamic factor. Finally, carrying out some computations, the effects of the non-homogeneity of the orthotropy ratio and the axial loading parameter on the critical parameters have been studied. Comparing results with those in the literature validates the present analysis.