Application of transformed differential quadrature to free vibration analysis of FG-CNTRC quadrilateral spherical panel with piezoelectric layers

In this work, a framework based on the differential quadrature (DQ) method for the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) quadrilateral spherical panels with surface-bonded piezoelectric layers is developed. The higher-order shear deformation theory is used to model the displacement fields of quadrilateral thin-to-moderately thick spherical panels. Hamilton's principle together with Maxwell's equation is applied to drive the differential governing equations and the related boundary conditions. The transformed differential quadrature (TDQ) method for the case of quadrilateral panels is established to discretize the governing partial differential equations. The benefit of this method is the usage of the transformed weighted coefficients, which are able to discretize partial differential equations in physical domain. This study exhibits that the TDQ approximation method shows a good convergence rate for quadrilateral curved panels. Furthermore, the accuracy and reliability of the proposed method are verified by comparing the results with the existing reference solutions or the results calculated by ANSYS software. The effects of CNTs volume fractions, CNTs distributions through the thickness, different boundary conditions and various panel geometrical parameters such as the panel thickness, piezoelectric thickness, side angle, and radius to length ratio on the natural frequency parameters are demonstrated. The article presents useful results for the design purpose of curved panels with complex geometries, for instance, achieving the optimal panel shape in order to pursuit the maximum structural stiffness. (C) 2018 Elsevier B.V. All rights reserved.