A numerical study on the free vibrations of nanocomposite conical panels with variously shaped cutout

Presented herein is a novel numerical approach for the vibrational analysis of conical panels with arbitrary-shaped holes made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) within the framework of higher-order shear deformation theory (HSDT). The developed approach can be called variational differential quadrature finite element method (VDQFEM) as it is based on the ideas of VDQ and finite element methods. The governing equations are obtained by means of Hamilton’s principle. Also, the relations of paper are presented in a new matrix–vector form which can be efficiently utilized in the coding process of numerical techniques. By VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element to derive the mass and stiffness matrices. Finally, the assemblage procedure is followed for obtaining total mass and stiffness matrices. Due to using HSDT, a novel mixed formulation approach is also proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Conical panels with square/circular/elliptical cutout and with crack are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the resonant frequencies of panels subject to various boundary conditions are investigated.