The Ritz formulation applied to the study of the vibration frequency characteristics of functionally graded circular cylindrical shells

AbstractIn this article vibration frequencies of functionally graded circular cylindrical shells are analysed and studied using the Ritz formulation. Since closed-form solutions are limited to simple cases, an approximate method is employed to solve the shell problem, and numerical evaluation is carried out using a direct variational method. Axial modal dependence is chosen in terms of Ritz polynomials to ascertain a rapid convergence of the method. Sanders and Budiansky's thin shell theory is utilized for strain—displacement and curvature—displacement relations. Functionally graded material characteristics for the constituent materials are distributed in accordance with a volume fraction law. Influence of boundary conditions and volume fraction exponents on the vibration frequency spectra is analysed. The present results are compared with some previous works and excellent agreement is found.