Modified Couple Stress Theory for nonlinear primary resonance of FG-GPLRC cylindrical shells in thermal environment

A modified couple stress theory (MCST)-based microshell model for functionally graded graphene platelets reinforced composite (FG-GPLRC) is proposed for the first time to investigate the nonlinear forced vibration behavior of reinforced microshells subjected to extreme temperatures. To achieve this, the effective elastic modulus is derived using the modified Halpin-Tsai model, while the rule of mixtures is applied for density, Poisson's ratio, and thermal expansion coefficients. The first-order shear deformation theory (FSDT) and von Karman strains are considered, and nonlinear governing partial differential equations (PDEs) are derived using Hamilton's principle, which accounts for size effects and initial stresses induced by the thermal environment. The Galerkin method, coupled with the multiple timescale method (MSM), is employed to solve the PDEs and obtain the nonlinear frequency-amplitude curve for primary resonance. The accuracy of the method is validated by comparison with previous research. The study examines the influence of GPL weight fraction, thickness distribution, temperature variations, geometric ratios, and material length scale parameters on the amplitude-frequency curves of nanocomposite cylindrical microshells. The results show that increasing the GPL content and the material length scale parameter leads to higher resonance frequencies. Additionally, while the small-scale parameter amplifies nonlinearity, an increase in the GPL content, especially near the inner and outer surfaces of the shell, reduces the nonlinearity of the reinforced composite. These findings provide valuable benchmarks for evaluating the performance of alternative methods.