Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods

Abstract

In this paper, free vibration analysis of fiber reinforced composite (FRC) conical shells resting on Pasternak-type elastic foundation is investigated. Two kinds of fiber distribution in the thickness direction, namely, uniformly distributed and functionally graded are considered. The material properties of FRC conical shells are estimated through a volume fraction power law. The equations of motion are derived through variational formulation. The governing equations are developed based on the classical shells theory and Sanders assumptions. Galerkin and Ritz methods are employed to solve the governing equations and determine natural frequencies of the conical shell. The conical shell assumed to be clamped at the both ends. Results are presented on the effect of fiber volume fraction, semi-vertex angle, thickness to radius ratio and elastic foundation stiffness parameters on the frequency characteristics of the conical shells. A comparative study between Ritz and Galerkin methods is carried out. Validity of the present study is confirmed by comparing the results with the data available in the open literature for a special case. A good agreement is observed between them.