Free nonlinear vibration analyzing of annular sector plate in contact with fluid

In this study, the nonlinear vibration of the annular sector plate in contact with fluid is investigated. The displacements in polar coordinates are considered in terms of the first order shear deformation theory. The strains are determined based on Von-Karman relationships. By considering the kinetic and potential energies and the Hamilton principle, the governing equations of motion are determined. The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. The shape modes are considered based on linear vibration modes. By using shape modes and Galerkin method, the governing equations have become nonlinear differential equations based on time. The nonlinear differential equations solved based on perturbation method and nonlinear natural frequency is determined. At the end, the numerical results are presented for a sample plate and the effect of parameters such as aspect ratio, sector angle, boundary conditions, fluid density and fluid height have been investigated. Also, the results obtained are verified with the current research (DQM method) and FEM, which shows good convergence.