Nonlinear size-dependent dynamic buckling analysis of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory

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.