Asymptotic and numerical analysis of free low-frequency ring-stiffened shells vibrations

Small free low-frequency vibrations of ring-stiffened cylindrical shells are considered. This problem is reduced to solution of the eigenvalue problems of linear differential equations. The equations describing the vibration of thin shells contain the dimensionless shell thickness as a small parameter. It allows to find the solution of the initial eigenvalue problem as the sum of slowly varying functions and edge effect integrals. Thus the initial system of differential equations is transformed into an approximate system of the smaller order. The simple asymptotic formulas for low frequencies are derived. Numerical results are obtained with the help of a shooting procedure. The asymptotic and numerical results converge.