Variable Stiffness and Free Vibration Analysis of Cylindrically Curved Plate with Variable Thickness Graphene Reinforced Porous Material

This paper investigates the free vibration problem of variable thickness graphene-reinforced porous cylindrical curved plates, which is limited by simply supported boundary conditions. The cylindrical curved plate consists of graphene platelets (GPL) and porous aluminum foam. To improve its performance, the graphene-reinforced porous cylindrically curved plate is approximated as a functional gradient layered structure. The cylindrically curved plate structure has a varying thickness in the radial direction, which can affect its stiffness.

The nonlinear dynamic equations of the cylindrically curved plate structures with variable thickness are obtained by employing the improved Halpin–Tsai model, mixing rule, first-order shear deformation theory (FSDT), and Hamilton's principle. Finally, the natural frequencies of the system are obtained by Navier’s method.

Several factors, including the distribution pattern of GPL, the pore’s distribution mode, the mass fraction of graphene, the subtended angle, the thickness function’s exponent, the radius-to-thickness ratio and length-to-thickness ratio, are considered for determining their impacts on the natural frequencies and modal shapes of variable-thickness graphene-reinforced porous cylindrically curved plates.