Three-dimensional free bending vibrations of variable radius functionally graded circular column immersed in infinite fluid

Abstract

The three-dimensional free bending vibrations of variable radius functionally graded circular column fully or partially immersed in infinite fluid are investigated for the first time using a coupled hierarchical finite-infinite element method based on curved elements. The fluid is incompressible, irrotational, and inviscid. The material properties vary continuously along the radial direction according to a simple power law function. The solid and fluid behaviors are described by the three-dimensional elasticity theory and Laplace’s equation, respectively. Coupling occurs on the interface via the boundary restraints imposed on it. Curved edges are described exactly by the blending functions. Examples of clamped-free and clamped-guided functionally graded circular columns with quadratic and cubic radius variations are used to illustrate the method. Convergence test and comparison study are conducted. New results for the frequencies of the lowest two bending modes are provided, which may serve as benchmark solutions. Furthermore, a parametric study is conducted to show the effects of various geometrical and mechanical parameters on the frequencies, modal deflections, and modal hydrodynamic pressures.