Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution

In this research, the free vibration analysis of simply supported rotating cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and non-uniform stiffeners spacing distribution is investigated. Ritz method is applied while stiffeners are treated as discrete elements. In strain energy formulation, by adopting Sander's theorem, stretching and bending characteristics of shells are considered. Also stretching, bending and wrapping effects of stiffeners are investigated. The translational inertia in three directions for shell and stiffeners, and rotary inertia for stiffeners are considered. The effects of initial hoop tension, centrifugal and Coriolis forces due to the rotation of shell are studied. The polynomial functions are used for Ritz functions. Natural frequency results for rings with uniform spacing and constant eccentricity have been compared with analytical and experimental results of other researchers, which showed good agreement. Fortunately, the agreements of the presented analytical results with the experimental values are better than the analytical values. At constant total mass of stiffeners, the effects of non-uniform eccentricity distribution and non-uniform rings spacing distribution (separately and simultaneously) on natural frequencies are investigated. Moreover, the influence of rotating speed on natural frequencies for the so-called non-uniform stiffeners distribution is studied.