This paper investigates the dynamic buckling of bi-directional (BD) functionally graded (FG) porous cylindrical shells for various boundary conditions, where the FG material is modeled by means of power law functions with even and uneven porosity distributions of ceramic and metal phases. The third-order shear deformation theory (TSDT) is adopted to derive the governing equations of the problem via the Hamilton’s principle. The generalized differential quadrature (GDQ) method is applied together with the Bolotin scheme as numerical strategy to solve the problem, and to draw the dynamic instability region (DIR) of the structure. A large parametric study examines the effect of different boundary conditions at the extremities of the cylindrical shell, as well as the sensitivity of the dynamic stability to different thickness-to-radius ratios, length-to-radius ratios, transverse and longitudinal power indexes, porosity volume fractions, and elastic foundation constants. Based on results, the dynamic stability of BD-FG cylindrical shells can be controlled efficiently by selecting appropriate power indexes along the desired directions. Furthermore, the DIR is highly sensitive to the porosity distribution and to the extent of transverse and longitudinal power indexes. The numerical results could be of great interest for many practical applications, as civil, mechanical or aerospace engineering, as well as for energy devices or biomedical systems.

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This article presents an analysis on the nonlinear dynamic buckling of a micro cylindrical shell reinforced by carbon nanotubes (CNTs) with considering agglomeration effects. The structure is surrounded by an elastic medium and is subjected to magnetic field and harmonic mechanical load. Mindlin theory is employed to model the structure and the modified strain gradient theory (SGT) is also used to capture the size effect. Mori-Tanaka approach is used to estimate the equivalent material properties of the nanocomposite cylindrical shell and consider the CNTs agglomeration effect. The motion equations are derived using Hamilton's principle and the differential quadrature method (DQM) along with Bolotin method is employed to solve them for obtaining the dynamic stability region. The effect of different parameters including magnetic field, CNTs volume percent and agglomeration effect, boundary conditions, elastic medium, size effect and length to thickness ratio on the dynamic buckling behavior of the system is studied. The results indicate that considering elastic medium, magnetic field and size effects, increases the stiffness of the structure and so, the dynamic instability region occurs at higher frequency while considering the CNTs agglomeration effect has inverse effect. Also, by increasing the CNTs volume percent and considering the clamped-clamped boundary condition, the dynamic behavior of the system improves.

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including [Formula: see text]-pattern, [Formula: see text]-pattern, [Formula: see text]-pattern, [Formula: see text]-pattern, and [Formula: see text]-pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium’s parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs.