Axisymmetric transverse vibrations of circular cylindrical shells with variable thickness

In this study, analytical solutions for axisymmetric transverse vibration of cylindrical shells with thickness varying monotonically in arbitrary power form due to forces acting in the transverse direction are derived for the first time, in terms of generalized hypergeometric function. To illustrate the use of the closed form solutions presented, free vibration analyses of a cylindrical shell with thickness variation under simply supported and clamped ends conditions are performed. The benchmark solutions may be used to check against numerical solutions for analysis of shells under dynamic load.