Linear and nonlinear vibrations of graphene platelet reinforced composite tapered plates and cylindrical panels

Abstract

The linear and nonlinear vibrations are investigated for the graphene platelet (GPL) reinforced composite tapered plate and cylindrical panel subjected to the transverse excitation by considering different boundary conditions. Functionally graded layer-wise structure is proposed to achieve the best performance by dispersing more GPLs in the most needed areas. Due to different distribution patterns of GPLs (D1, D2, D3 and D4), the modified Halpin-Tsai model and the rule of mixture are adopted to predict the effective material properties. Vibration characteristics of the composite tapered plate and cylindrical panel characterized by natural frequencies and mode shapes are obtained through the first-order shear deformation theory (FSDT) in conjunction with the Chebyshev-Ritz method. Lagrange's formulation is adopted to derive nonlinear governing equations of the composite tapered plate and cylindrical panel. At first, a series of comparisons are performed to ensure the accuracy of the proposed models and present method. Then, comprehensive results are given in the form of natural frequencies and mode shapes to report the parametric studies of free vibrations for the composite tapered plate and cylindrical panel. Noting that the frequency loci veering phenomenon and the corresponding mode shape shift phenomenon are revealed. Last, special attention is given to nonlinear dynamics of the GPL reinforced composite tapered cylindrical panel.