A semi-analytical method for vibration analysis of functionally graded (FG) sandwich doubly-curved panels and shells of revolution

Abstract

In this paper, a semi-analytical method is described and applied to investigate the free vibration of the functionally graded (FG) sandwich doubly-curved panels and shells of revolution with arbitrary boundary conditions, in which the first-order shear deformation theory is considered. Two types of sandwich models and four kinds of common functionally graded distribution, which determine the mechanical properties, are considered in the theory model process. In despite of the external factors which consist of boundary conditions, geometric model, material constants and so on, each of the unknown displacement functions of the FG sandwich doubly-curved panels is expanded as a novel Fourier series expression. Since the auxiliary function is introduced in the Fourier series expression, it can remove any potential discontinuities of the original displacement and its derivatives at the edges and it also has excellent convergence, accuracy, stability and a wide range of the boundary conditions including the simple classical boundary conditions, general elastic restraints and their combining cases. The linear vibration information including the natural frequency together with the mode shapes of the FG sandwich doubly-curved panels is obtained by means of the Ritz-variational energy method. A number of examples of the FG sandwich doubly-curved panels and shells are examined to assess the convergence, accuracy and stability of the current solutions, and then the first known results with various boundary conditions, geometric and material constants are presented. Additionally, the parameter studies of the FG sandwich doubly-curved panels and shells are also reported.