Free vibration analysis of circular cylindrical shell with non-uniform elastic boundary constraints

• Free vibration of cylindrical shell with non-uniform elastic boundary constraints is analyzed.
• The exact series solution is obtained by the improved Fourier series method.
• The change of boundary conditions can be easily achieved by varying the stiffness of boundary springs.
• Numerical examples are presented to illustrate the effects of some interesting and practically important boundary restraints.

As far as the study of circular cylindrical shell is concerned, most of the existing works are limited to classical homogeneous boundary conditions. However, complicated boundary conditions, such as elastic and non-uniform boundary conditions are encountered in many engineering applications. Thus, it is of important practical significance to investigate the vibrations of cylindrical shell with this kind of boundary conditions. This paper is mainly concerned with the free vibrations of cylindrical shell with non-uniform elastic boundary constraints. The exact solution for the problem is obtained using improved Fourier series method, in which each of three displacements of the shell is represented by a Fourier series supplemented by several terms introduced to ensure and accelerate the convergence of the series expansions. The unknown expansions coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz procedure. The change of the boundary conditions can be easily achieved by only varying the stiffness of the four sets of boundary springs at each end of the shell without the need of making any change to the solution procedure. The excellent accuracy of the current results is validated by comparison with the finite element method (FEM) results. Numerical results are presented to illustrate the effects of some interesting and practically important boundary restraints on free vibrations of circular cylindrical shell, including varying stiffness of boundary springs, point supported and partially supported boundary conditions.