Multiple scale-Galerkin's hybrid method for nonlinear frequency analysis of honeycomb cylindrical panels bonded to agglomerated CNT-reinforced patches

Honeycomb structures are a category of lightweight materials distinguished by a distinctive geometric configuration that resembles a honeycomb. On the other hand, carbon nanotube-reinforced composites (CNT-RCs) have developed as innovative materials owing to carbon nanotubes' remarkable mechanical, thermal, and electrical capabilities. Consequently, this work gives, for the first time, a nonlinear vibration analysis of a sandwich cylindrical panel. The panel's core consists of honeycomb structures, while the patches comprise CNT-RC. The nanotubes are presumed to be randomly distributed throughout the patches; hence, the impact of their agglomeration is examined using the Mori–Tanaka micromechanical method. First-order shear deformation theory serves as the displacement field to determine the fundamental relations of the equations of motion. Furthermore, von Karman nonlinear strains are utilized to address geometric nonlinearity. The Hamilton's principle is employed to regulate the partial equations of motion. The Galerkin method is utilized to transform the equation of motion into a nonlinear motion equation. The nonlinear motion equation is subsequently resolved using the multiple scale approach. The influence of numerous factors, including the geometrical characteristics of the honeycomb core, the mass percentage of CNTs, agglomeration parameters, other physical parameters, and initial conditions on the outcomes, is examined.