The effect of uncertainty sources on the dynamic instability of CNT-reinforced porous cylindrical shells integrated with piezoelectric layers under electro-mechanical loadings

Abstract

In the present study, the influence of the propagation of different uncertainty sources on the dynamic stability of a sandwich carbon nanotube-reinforced (CNT) cylindrical shell under a pulse axial load is investigated. The core of the cylindrical shell is composed of a porous metal matrix reinforced with CNTs. The core is surrounded by piezoelectric layers. Five distributions of CNT reinforcements in the shell thickness are considered in this study. Moreover, it is assumed that the shell rests on an elastic foundation. Two dynamic curves and the Chebyshev model are combined to examine the dynamic stability probability of functionally-graded carbon nanotube-reinforced cylindrical shells surrounded by piezoelectric layers (FG-CNT-P). The stability of the shell is investigated under both mechanical dynamic load and electrical potential. The effective material properties of the functionally graded carbon nanotube shells are estimated through a micromechanical model based on the extended rule of mixture. The virtual work method based on Sanders’ nonlinear theory and the higher-order shear deformation theory is used to derive the dynamic equilibrium equations of the CNT cylindrical shells surrounded by piezoelectric layers and an elastic medium. The Fourier differential quadrature method is used to solve these equations. The analysis results are presented in terms of the probabilistic density functions (PDFs) of the buckling loads of the composite shells. Accordingly, the probabilistic distributions of the buckling loads of the shells corresponding to the first three modes of buckling are overlapping. Hence, the first mode of buckling determined in a deterministic study may not always be the dominant failure mode of the structure. Consequently, a great attention is paid to this phenomenon and the effects of different factors on it. Finally, the sensitivities of the critical loads of the FG-CNT-P cylindrical shells to different sources of uncertainty are assessed through a sensitivity analysis.