Free vibration analysis of functionally graded graphene platelets – reinforced composite conical shell panels with different boundary conditions

This paper analyses the free vibration behavior of truncated conical panels made of a polymeric matrix reinforced with graphene platelets (GPLs). Distribution of GPLs across the thickness of the panel is considered uniform or functionally graded. The mechanical properties of the composite have been calculated using the modified Halpin-Tsai model and the rule of mixtures. Considering strain- displacement relationships as well as first order shear deformation theory (FSDT) of shells, the governing equations have been derived using Hamilton principle. In the next step, to obtain the natural frequencies of the structure, the governing equations have been discretized and solved using Chebyshev polynomial of the first kind and Ritz method which is suitable for structures with different boundary conditions. Comparison of the numerical results of this study with other articles show that the numerical results are highly accurate. Also, parametric studies have been performed to investigate the effect of GPLs distribution patterns, GPLs weight fraction, different boundary conditions, different geometric parameters on the vibrational behavior of the conical panel. The results show that the use of GPLs as a reinforcement for the nanocomposite panel is effective to improve the vibrational behavior and greatly increases the stiffness and resistance of the panel.