Application of a semi-analytical method to the dynamic analysis of functionally graded porous conical–conical–cylindrical shell

The dynamic response characteristics of a coupled, functionally graded porous conical–conical–cylindrical shell (FGP-CCCS) with arbitrary boundary conditions are investigated using a semi-analytical method in this research. The individual shells are firmly connected at the interface. It is assumed that FGP-CCCS is made of three types of FGP materials with uniform or non-uniform distribution of porosity along the thickness direction. The overall theoretical model for the dynamic response analysis of FGP-CCCS is established based on the first-order shear deformation theory. All the displacement components of individual shells, including boundary conditions, are expanded along the meridian direction into the Chebyshev polynomial and along the circumferential direction into the standard Fourier series. By applying the Rayleigh–Ritz method to the determination of the expansion coefficient, a unified solution for a FGP-CCCS with arbitrary boundary conditions is derived directly without the need to change the equation of motion or the displacement functions. The reliability and accuracy of this method is verified in comparison with the results in the literature and finite element method. New numerical examples are presented to illustrate the dynamic response characteristics of FGP-CCCS, and the effects of the geometrical, material parameters and external forces on the dynamic response of FGP-CCCS with different boundary conditions are reported.