Stability analysis of rectangular parallel plates interacting with internal fluid flow and external supersonic gas flow

In this paper, we analyze the dynamic stability of deformable rectangular plates (single and two parallel) that interact simultaneously with the external supersonic gas flow and the internal flow of an ideal fluid. The mathematical formulation of the dynamics of elastic structures is made using the variational principle of virtual displacements, which includes the expression for the work done by aero- and hydro-dynamic forces. The motion of the liquid in the case of small perturbations is described by the equations of potential theory, which are converted to a weak form using the Bubnov-Galerkin method. Numerical solution of the problem is based on the application of the procedures of the finite element method to the coupled system of equations. The estimation of stability involves computation and analysis of complex eigenvalues, obtained at gradually growing velocity of the fluid or gas flow. The diagrams showing the mutual influence of fluid and gas flow velocities on the boundary of aero-hydroelastic stability, are constructed and the effects of the kinematic boundary conditions specified at the edges of the structure and the height of the fluid layer are evaluated. It has been established that the violation of smoothness of the obtained dependences and stability diagrams can be attributed either to a change in the vibration mode, or to a change in the type of stability loss.