Free vibration of variable thickness FGM beam submerged in fluid

This paper studies the free vibration of the variable thickness beam made of functionally graded materials (FGMs) which is submerged in fluid. It is assumed that material properties follow the power law distribution along the thickness direction. In this fluid-structure interaction problem, the added mass method is introduced to express the effect of the hydrodynamic loading on FGM beams. Based on the Timoshenko beam theory, the governing equations and boundary conditions are derived by using Hamilton's principle. The differential quadrature (DQ) method is employed to discretize the governing equations and boundary conditions, which are then calculated to determine the natural frequencies and mode shapes by using a direct iterative method. Numerical results are conducted to discuss the influences of the fluid density, non-uniform parameter of thickness, different types of thickness variation, gradient index and slenderness ratio on the vibration characteristic of FGM beams.