The effect of fluid column pressure on the natural frequencies of an annular sector plate made of functionally graded material

In this study, the effect of fluid dynamic pressure on the linear vibrations of annular sector plate made of Functionally Graded Material (FGM) is investigated. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT) with consideration of rotational inertial effects and transverse shear stresses. The governing equations of motion of the plate are derived by considering the kinetic and potential energies and using the Hamilton’s principle. Also, the pressure applied from the fluid to the plate is determined by solving the velocity potential function of the fluid and the velocity equality at the contact surface of the fluid and the sector in terms of vertical displacement of the sector. The shape of the studied plate modes is based on satisfying the boundary conditions of the plate. By placing hypothetical modes, harmonic responses and using the Galerkin method, the governing equation have become the characteristic equation and by using the semi-analytical method that used for all boundary conditions, the natural frequencies are obtained. Furthermore, the numerical results are presented for a sample plate and the effect of different parameters such as sector angle, boundary conditions, fluid density, and fluid height is investigated. Finally, the obtained results are validated without considering the fluid with previous researches, and in case of contact with the fluid with finite element model (ANSYS software).