Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints

In the present work, a three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints is presented. The last two structures are obtained as special cases of the conical shell. The effective material properties of functionally graded structures vary continuously in the thickness direction according the general four-parameter power law distributions in terms of volume fraction of constituents, and are estimated by Voigt's rule of mixture. The exact solution is obtained by means of variational principle in conjunction with modified Fourier series which is composed of a standard Fourier series and some auxiliary functions. Validity and accuracy of the current method are demonstrated by comparing the present solutions with existing results. Numerous new results are given for functionally graded conical, cylindrical shells and annular plates with various boundary conditions including classical and elastic boundary conditions. Parametric investigations are carried out to study the effects of geometrical parameter, boundary conditions and material profiles on free vibration of functionally graded structures.