Nature of Supersonic Flutter of Aero-Magneto-Elastic System at Pre-Critical Flowing Speeds

In this paper the joint effect of non-linear supersonic flutter of isotropic dielectric plate and the presence of a longitudinal magnetic field is investigated, the nature of dependence of amplitude of flutter type oscillations on the frequency of oscillations in a subcritical state is investigated and especially the effect of the applied magnetic field on the noted dependence is studied. The system of non-linear differential equations is derived. In case of linear problem, the obtained results show, that: in the presence of the magnetic field the critical flutter speed decreases; magnetic field narrows the stability area; the larger is the number of circumferential waves, the larger is the value of critical flutter speed; the larger the value of aspect ratio of the plate, the smaller the value of the critical flutter speed; the thinner the plate, the smaller the value of critical flutter speed; the thinner the plate, the greater the value of aerodynamic pressure. The magnitude of the aerodynamic pressure, determined for the fixed flow speed, and taking into account the presence of magnetic field, is higher when compared with the appropriate value of aerodynamic pressure determined on the basis of classical formula without magnetic field; for fixed thickness of the plate, the larger the aspect ratio, the larger the value of aerodynamic pressure. Also in this case, the magnitude of aerodynamic pressure and the value of flowing stream are inversely proportional; the higher the plate’s aspect ratio, the stronger the effect of the magnetic field; the aerodynamic pressure monotonically decreases for increasing number of half-waves and, as the flow speed increases, the magnitude of aerodynamic pressure is lower for the same number of half-waves; the magnetic field does increase the aerodynamic pressure for the same number of half-waves for a plate with fixed geometrical parameters.