Aeroelastic stability of plate interacting with a flowing fluid

The paper presents the results of a numerical study of the dynamic behavior of the deformable plate interacting both with the external supersonic gas flow and the internal fluid flow. The constitutive relations describing the behavior of ideal compressible fluid in the case of small perturbations are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The aero- and dynamic pressures are calculated based on the quasi-static aerodynamic theory. The strains in the plate evaluated following the Timoshenko hypotheses. A mathematical formulation of the dynamic problem of elastic structure is developed using the variational principle of virtual displacements, which takes into account the work done by the inertia forces, aerodynamic and hydrodynamic pressures. Calculation of complex eigenvalues of the coupled system of two equations is performed using an algorithm based on implicitly restarted Arnoldi method. The stability criterion is based on an analysis of the complex eigenvalues of system of two equations obtained for increasing flow or gas velocity. The reliability of the obtained numerical solution has been estimated by comparing it with the available theoretical data. A few numerical examples were considered to demonstrate the existence of different types of instability depending on the velocities of fluid or gas flow, combinations of kinematic boundary conditions prescribed at the edges of the plate, and the fluid layer height. It has been found that a violation of the smoothness of the obtained relationships and diagrams of stability is caused by a change in the flutter mode, or change of the type of loss of stability.