Issues of dynamics of conductive plate in a longitudinal magnetic field

Abstract

On the basis of Kirchhoff hypothesis the problem of vibrations of conductive plate in a longitudinal magnetic field is brought to the solution of the singular integral–differential equation with ordinary boundary conditions. The formulated boundary-value problem solved and the influence of magnetic field on the characteristics of vibration process of the examined magnetoelastic system is investigated. Via the analysis of obtained solutions it is shown that the presence of magnetic field can: (a) increase essentially the frequency of free magnetoelastic vibrations of the plate; (b) decrease essentially the amplitude of forced vibrations if r⩽1 , where r=θ/ω,θ – is the frequency of acting force, ω – is the frequency of own vibrations of the plate magnetic field is being absent; (c) increase essentially the amplitude of forced vibrations if r>1; (d) decrease essentially the width of main areas of dynamic instability. It is shown that: (1) in the case of perfectly conductive plates magnetic field constricts essentially the width of main area of dynamic instability; (2) if plate’s material has the finite electroconductivity, then the certain value of the intensity of external magnetic field exists, exceeding of which excludes the possibility of appearance of parametric type resonance. It is shown also that in dependence on the character of initial excitements the plate can vibrate either across the initial non-deformable state, or across the initial bent state.