In this paper, a 3D semi-analytical method is proposed by introducing the Durbin’s Laplace transform, as well as its numerical inversion method, state space approach and differential quadrature method to analyse the transient behaviour of functionally graded material cylindrical panels. Moreover, to investigate the effectiveness of the proposed semi-analytical solution, four boundary conditions are used to undertake the analyses. Comparing the proposed approach with other theoretical methods from the literatures, we see better agreements in the natural frequencies. Besides, the semi-analytical solution acquires nearly the same transient response as those obtained by ANSYS. Convergence studies indicate that the proposed method has a quick convergence rate with growing sample point numbers along the length direction, so do layer numbers increase along the radial direction. The effects of thickness/outer radius ratio, length/outer radius ratio and functionally graded indexes are also studied. When carbon nanotube is added to functionally graded material cylindrical panel, the composite structures have been reinforced greatly. The proposed 3D semi-analytical method has high accuracy for the analysis of composite structures. This study can serve as a foundation for solving more complicated environments such as fluid–structure interaction of flexible pipe or thermal effect analysis of functionally graded material in aerospace field.
Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions
