Critical Velocity of Potential Flow in Interaction With a System of Plates

The elastic structures subjected to flowing flow can undergo the excessive vibrations and consequently a considerable change in their dynamic behavior, and they may lose their stability. A fluid-solid finite element model is developed to model a set of plates subjected to flowing fluid under various boundary conditions, fluid level, and fluid velocity that strongly influence the dynamic behavior of the plates. A hybrid method, which combines the finite element approach with the classical theory of plates, is used to derive the dynamic equations of the coupled fluid-structure system. The membrane and the transversal displacement fields are modeled, respectively, using the bilinear polynomials and the exponential function. The structural mass and rigidity matrices are derived by exact integration of developed displacement field. The fluid pressure is expressed by inertial, Coriolis and centrifugal fluid forces written, respectively, as a function of acceleration, velocity and transversal displacement. The fluid dynamic pressure is determined using the potential flow equation. Integrating this dynamic pressure in conjunction with the structural element results in the flow-induced mass, damping, and stiffness matrices, hence, one can establish the dynamic equations of coupled fluid-structure system. The impermeability condition that ensures the permanent contact between the shell and the fluid is applied at the contact surface. A parametric study has been performed to investigate the effect of physical and geometrical parameters (e.g. boundary conditions, fluid level, and flow velocity) on the dynamic response of the coupled system. The results are in satisfactorily agreement with those of experiments and other theories.