Free Vibration of Functionally Graded Porous Conical Panel Reinforced with Graphene Platelets

The study presents the free vibration characteristics of a conical panel reinforced with graphene platelets (GPL) and functionally graded (FG) porous material. The effective mechanical properties are evaluated using an extended rule of mixture in conjunction with a modified Halpin-Tsai micromechanics model and the mechanical properties of open-cell metal foams. The governing equations are derived based on the strain-displacement relationships and the first-order shear deformation theory (FSDT) using Hamilton's principle. The natural frequencies of the structure are obtained by discretizing and solving the governing equations using Chebyshev polynomials and the Ritz method, which is suitable for structures with different boundary conditions. A comparison of the numerical results with other studies demonstrates their high accuracy. Additionally, parametric studies are conducted to investigate the impact of porosity distribution, GPL distribution patterns, GPL weight fraction, different boundary conditions, and porosity coefficient on the vibrational behavior of the conical panel. The results indicate that an increase in the weight fraction of graphene nanochips leads to an increase in the bending stiffness of the panel and the dimensionless natural frequency parameter. Furthermore, the dimensionless natural frequency decreases slightly with an increase in the porosity coefficient in the conical panel with PD-X porosity distribution, whereas in the conical panel with PD-O and PD-UD porosity, the dimensionless natural frequency and stiffness decrease significantly with an increase in the porosity coefficient.

کلیدواژه ها:

Graphene Platelets ، porous Conical Panel ، Ritz method ، Chebyshev polynomials