The effects of magnetic field on supersonic flutter characteristics of dielectric plate: Dependence amplitude-speed

Abstract

For aircraft design, design of the wing shape (for example, as a panel) is critical as it affects aerodynamic performance. In case, when panel is made of a material with magnetic properties, magnetic field of different origin plays an important role. As aircraft designers strive for improved efficiency and performance, accurate prediction of magneto-aeroelastic effects is becoming a necessity. For example, while high aspect ratio wings have higher aerodynamic efficiency, the structural deformation of the wing under the influence of both aerodynamic load and magnetic field is no longer negligible and a coupled analysis needs to be carried out to during the design phase.

This paper offers the authors’ views on critical magneto-aeroelastic behavior for dielectric rectangular isotropic plates and is a continuation of the work (Baghdasaryan et al., 2023): “Supersonic flutter characteristics of dielectric rectangular plate: The effects of magneto-aero-hydrodynamic interactions, Journal of Fluids and Structures, 2023”.

The work "Supersonic flutter characteristics of dielectric rectangular plate: The effects of magneto-aero-hydrodynamic interactions" presents both, linear and non-linear flutter behaviour of an isotropic dielectrical plate streamlined by a perfectly conductive supersonic gas flow and immersed in a longitudinal magnetic field. It is assumed, that flowing liquid is an inviscid, non-heat-conducting one with infinite conductivity. For the first time, an analytical expression of the aerodynamic pressure accounting for an applied magnetic field is presented. This expression generalizes the formula of piston theory to account for magnetic field interactions. Based on the linear problem of aero-magneto-flutter, stability conditions are obtained and corresponding stability boundary is found. As a result, of the analytical description, the influence of magnetic field on the critical speed is investigated for different geometrical parameters and different parameters of the magnetic field. The influence of the number of modes on the critical flutter speed is investigated as well. It is shown, that the magnetic field decreases the stability boundary of a steady flutter type oscillations of rectangular plate.

Using the expressions for forces, acting on the body, and the theory of thin flexible plates the system of equations, describing vibrations and stability of plates, is obtained. Having solved the formulated boundary-value problems both qualitative and quantitative influence of magnetic field and flowing stream on the existence of non-linear flutter type oscillations and on the dependence of the amplitude of oscillations on the frequency for the fixed values of flowing stream are investigated. The presented work differs from the previous one in the subject of research. There are many studies in the scientific literature that study the amplitude-frequency dependence of both natural and forced oscillations. There are numerous studies of the amplitude-velocity relationship of flutter oscillations without taking into account the magnetic field.

In the presented work is devoted to filling this gap and the influence of a magnetic field on the nonlinear characteristics of supersonic flutter, namely on the amplitude-velocity dependence of nonlinear flutter oscillations is investigated.