Effects of in-plane inertia on natural frequency and stresses of long circular cylindrical shell

In this paper an analytical procedure is given to study the free-vibration characteristics of thin long circular cylindrical shells with simply supported boundary conditions. An approach based on Sander’s nonlinear theory and Lagrange equations is employed. Influence of in-plane inertia on natural frequencies and stress for several modes shape is discussed. Natural frequencies for a number of particular cases are evaluated and compared with some available experimental and other analytical results in the literature. The distributions of the bending and axial stresses associated with the nonlinear modes shape are given and compared with those obtained via the linear theory.