Nonlinear vibration analysis of a double curved shallow sandwich shell in which the core made of three-phase nanocomposite and the two-outer layer of electromagnetic materials

Abstract

This paper investigates the nonlinear vibrations of a double curved shallow sandwich shell with a three-phase nanocomposite core and two outer electromagnetic layers considering the thermal environment's influence. Relying on the Halpin–Tsai model, the core is assumed to be made of some composite plies incorporating three constituents: carbon nanotubes (CNTs) or graphene nanoplatelets (GPLs) as nanocomposites, fibers and polymeric matrix (resin). Governing equations calculating the nonlinear vibration of the double curved shallow shell were obtained by combining Reddy's first-order shear deformation theory (FSDT) and the Von Kármán geometrical nonlinearity. Later, this system of equations is transformed into the nonlinear ordinary differential expressions by utilizing the Galerkin procedure. Thus, the effects of material properties, temperature, geometrical properties, elastic foundations to the frequency of linear and nonlinear free vibration, and amplitude–frequency relations of the double curved shallow sandwich shell were discussed. The results demonstrate that the free vibration frequency of the shell increases if the magnetic field enhances, whereas that decreases when the voltage expands in both models as CNTs and GPLs. Simultaneously, the shallow shell has a better ability to force load compared to a plate with the same dimensions. These outcomes can make a profit in the design and manufacturing of new smart structures applied in energy harvesting, and medicine.