Abstract
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.
Highlights
Graded materials (FGMs), whose property gradient is caused by chemical composition, atomic order or microstructure, have attracted much attention of many groups.[1,2,3,4] Because of their advantageous stiffness-toweight ratio and strength-to-weight ratio as well as their tendency for high performance, Functionally graded materials (FGMs) structures play important roles in ocean engineering, fuselage and submarine components
It shows that the deflection of FGM cylindrical panels increases as length/outer radius ratio l/a increases
Compared with many numerical methods, the semi-analytical results in this paper have higher accuracy, because there are fewer errors and limitations caused by the introduction of stress and displacement assumptions
Summary
Graded materials (FGMs), whose property gradient is caused by chemical composition, atomic order or microstructure, have attracted much attention of many groups.[1,2,3,4] Because of their advantageous stiffness-toweight ratio and strength-to-weight ratio as well as their tendency for high performance, FGM structures play important roles in ocean engineering, fuselage and submarine components. Quan and Duc[10] investigated the dynamic response and nonlinear vibration of FGM thick shells through the use of third-order shear deformation shell theory. To consider various boundary conditions, the differential quadrature method (DQM) is effectively used to discretize the governing equations.[16] Based on the 3D elasticity theory, Alibeigloo et al.[17,18] analysed free vibration of FG cylindrical plates and shells embedded in piezoelectric layers by using SSM and DQM. Based on the elasticity theory and Hamilton’s principle, the transient response in thermal environment of multi-layered FG shells was presented by Malekzadeh et al.[29] Selahi et al.[30] developed a hybrid method by using 3D elasticity theory for dynamic behaviour of FG truncated conical shell, with DQM discretizing the governing equations in both spatial and time domains. Assuming the material of each layer is orthotropic among the coordinate planes, the linear stress–displacement relationships for an arbitrary layer can be expressed as the following matrix form
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