Ritz Method for Vibration Analysis of Cylindrical Shells with Ring Stiffeners

Abstract

It is generally perceived that it is awkward to automate the Ritz method for structural analysis because the Ritz functions that satisfy one combination of boundary conditions cannot be used for another. To handle general boundary conditions, analysts thus resort to the use of Lagrangian multipliers or discretization methods such as the finite-element method, finite-difference method, and the differential quadrature method. Contrary to the foregoing perception, this paper demonstrates the manner in which the Ritz method can be conveniently automated for the vibration analysis of cylindrical shells with varying ring-stiffener distribution. To achieve this, a set of Ritz functions is proposed that contains the boundary equations raised to appropriate integer powers so that the geometric boundary conditions are satisfied a priori. The presented Ritz formulation has been nondimensionalized to obtain generic solutions for shells with various stiffener distributions. Based on these solutions, the effects of stiffener eccentricity, number, sizes, and locations on the vibration frequencies were examined.