Nonlinear and linear free vibrations analysis of sandwich cylindrical shells with auxetic core and FG face sheets with different boundary conditions
Soheil Hashemi, Mohammadamin Forghani, Mahmoud Shadmani, Mohammad Hosein Ebrahimzadeh-Mardani
Abstract
Auxetic structures exhibit counterintuitive and intriguing behaviors due to their negative Poisson’s ratio. Unusual and practical dynamic and static properties resulting from the strange behavior of these structures have been reported to date. This article focuses for the first time on the relationship between the mechanical and structural properties of auxetic materials and important characteristics of nonlinear vibrations of auxetic-core sandwich cylindrical shells (AC-SCSs) and functionally graded (FG) face sheets under various boundary conditions. To this end, the mechanical properties of the auxetic core and FG skins are first calculated, and then, the dynamic equations of the shell are derived using the first-order shear deformation theory (FSDT) and the nonlinear von Kármán strain–displacement relations. A powerful and rapid generalized differential quadrature method (GDQM) is employed to compute the natural frequencies and mode shapes of the shell. Subsequently, the nonlinear natural frequency of the shell is calculated using the Galerkin and harmonic balance methods. For verification, the results of this study are compared with findings from previous research. Finally, the effects of parameters such as the geometry of the auxetic core cell, the FG power index, boundary conditions, and the aspect ratios of the shell on both linear and nonlinear frequencies, as well as the hardening behavior of the AC-SCSs, are examined. The results of this research provide a comprehensive and reliable benchmark for researchers studying AC-SCSs.