Stability of elastic and viscoelastic plates in a gas flow taking into account shear strains

Abstract

It is well known that the internal friction in a material can have a considerable destabilizing effect on the stability of non-conservative systems. Apart from the Voigt model, the viscoelastic body model is sometimes utilized to describe material damping. This relates the stability problem for non-conservative elastic systems with that for viscoelastic system. The Bubnov–Galerkin method is usually applied for solving the problems. In this case, the displacement functions are represented by series in terms of natural vibration modes ϕ i( x ) of the elastic system. To provide a high degree of accuracy for the solution, one should involve a fairly large number of modes. For a viscoelastic plate, the number of terms to be kept in the expansion of the deflection can be substantially more. One should bear in mind, however, that as the number of modes preserved in the expansion increases, the influence of shear strains and rotational inertia on the behavior of the solution becomes more pronounced. In view of this, it is important to study the stability of non-conservative viscoelastic systems with the shear strain and rotational inertia being taken into account. In the present paper this problem is solved for a viscoelastic plate in a supersonic gas flow.