Three-dimensional free flexural vibrations of fluid-filled functionally graded circular cylindrical shell with curvilinear radius variation

Abstract

The three-dimensional free flexural vibrations of functionally graded circular cylindrical shell with curvilinear radius variation fully or partially filled with incompressible and inviscid fluid are investigated for the first time using a coupled axisymmetric solid-fluid hierarchical finite element method based on curved elements. Curved edges are described exactly by means of blending functions. The method is used in conjunction with the three-dimensional elasticity theory and Laplace’s equation to obtain the governing equations. The material properties follow the power law distribution in the thickness direction. The effectiveness of the method is illustrated using examples of clamped-free and clamped-guided functionally graded circular cylindrical shells with quadratic and cubic radius variations. The method is validated through convergence test and comparison study. New results for the cycle frequencies of the lowest two flexural modes are presented, which may serve as benchmarks for future studies. Moreover, the effects of several geometrical and mechanical parameters on the cycle frequencies, modal deflections, and modal hydrodynamic pressures are explored.