Stability of a dielectric rectangular plate in a longitudinal magnetic field in the presence of a supersonic flow field

In this paper, we investigate the critical magneto-aeroelastic behavior of dielectric rectangular isotropic plates. The incident flow of a perfectly conducting supersonic gas and a magnetic field cause the perturbed pressure, which we can determine using magneto-aero-elastic stability and dynamic models as well as find the critical flutter speed of the flowing stream. Here, we present the analytical description of the generalized formula of pressure obtained from the “piston theory” of the classical theory of gas dynamics for the case of elastic plates in a magneto-hydro-dynamic flow. We implemented some parametric studies to show the influence of the magnetic field on the flutter boundary. Influence of magnetic field on the dependency “amplitude–frequency” is investigated for several geometrical parameters of examined plate. It is shown that the noted dependency can be as a single-value, as well as a multi-value function. It is shown also that strong magnetic fields have a great influence on the nature of the amplitude–frequency dependence, which is inherent to the case of nonlinear natural oscillations of shells.