Stability analysis and optimization management of nanocomposites-reinforced panels using a thickness-dependent shear deformation theory and HDQM

Using the modified couple stress theory, this study investigates the nonlinear vibrations of a sandwich microshell composed of a functionally graded graphene platelets (FG-GPL)-reinforced core and two uniform outer skins, all simply supported. The analysis employs the first-order shear deformation shell theory alongside a nonlinear strain framework. The mechanical properties of the GPL-reinforced core are assumed to vary with thickness, utilizing the Halpin-Tsai model. Three distinct distribution patterns of GPLs throughout the thickness are examined. The microshell is subjected to thermal loading, facilitating the calculation of its temperature field across the thickness by applying the one-dimensional Fourier heat conduction equation, which accounts for thermal boundary conditions at both the inner and outer surfaces of the shell. The shell models incorporate shear deformation and rotary inertia, while geometric nonlinearity is addressed using the von Karman approach. The fundamental partial differential equations (PDEs) governing the system are derived using Hamilton's principle. These coupled PDEs are then transformed into a set of ordinary differential equations (ODEs) via the Galerkin method and solved using the multiple timescale method to obtain results. The findings are validated against existing literature, demonstrating a robust level of agreement. This study thoroughly examines the effects of various factors, including GPL weight fraction, thickness distribution patterns, material length scale parameters, core length, radius, and individual layer thickness on nonlinear frequency ratios, fundamental linear frequencies, and nonlinear frequencies.