Nonlinear vibrations of doubly curved micropanels reinforced by graphene nanoplates in length direction under non-uniform thermal loading

Abstract

Structures made of composites are quite common in different industries entailing automotive, marine, and aircraft industries, thanks to their favorable lightweight and strength. This study investigated the nonlinear vibrations of the various shapes of size-dependent graphene nanoplatelets reinforced micropanels under non-uniform thermal loading. In diverse ways in the axial direction, the material characteristics of graphene nanoplates (GPLs) alter. Taylor’s series expansion terms in curvature coordinates are used to illustrate the displacement field. Nonlinear von Karman theory and Hamiltonian principle work together to derive the nonlinear form of the pertinent equations and boundary conditions. Strain gradient theory with consideration for inherent length scale characteristics is investigated to account for size effects. By discretizing the spatial domain equations, deriving Duffing-type equations, and using Kronecker and Hadamard products, the governing equations and numerous nonlinear boundary edges are resolved. Using the techniques and answers outlined above, the results section is produced. There are four sections for this research. The findings are cross-checked with those from other studies that have been published in the first section. The effects of geometric and physical factors are shown in Parts 2, 3, and 4 on the nonlinear to linear frequency curve, the nonlinear frequency curve, and the sensitivity of the nonlinear frequency-to-size effect (SNFSE).