Analytical Study of Free Vibrations of Fluid Coupling and Structure in Collision of Turbulent Fluid with FGM Plate

In this paper, the free and forced vibration of a functional rectangular plate in contact with a turbulent fluid is investigated. Functional plates have been considered due to their high thermal resistance to residual stresses. The geometry of the problem is that one side of the reservoir in which the fluid is placed is covered with a plate of Functionally Graded Material (FGM). In order to approximate the displacement of the plate, assuming the third-order theory of shear deformation, trigonometric harmonic test functions are used, which determine the boundary conditions of the simple and fixed plate support. In the equations governing fluid oscillating behavior, the potential velocity of the fluid is obtained by determining the boundary conditions of the fluid in the form of February series functions. To achieve the natural frequency of the plate in contact with turbulent fluid and the shape of the vibrating mode, the Rayleigh-Ritz energy method is used based on the minimum potential energy. In order to check the accuracy of the method used, the results of analytical solution after solving the equations by coding in Wolfram Mathematica software have been compared with numerical solution of Abaqus software and then with accurate results in references, which shows the appropriate accuracy of the solution. Finally, the effect of volumetric coefficient parameters, volume ratio, length ratio, plate thickness ratio, fluid height, reservoir width and boundary conditions on the natural frequency of the plate in contact with turbulent fluid has been investigated and analyzed.