Dynamic stability of plate interacting with viscous fluid .
We consider the problem of stability of the motion of an deformable plate which is a part of the border dividing the areas filled with viscous incompressible fluid. Two models of a deformable solid are considered. The first (nonlinear) model of an elastic body takes into account the longitudinal and transverse deformation of the plate, but does not take into account its aging. The second (linear) model of a viscoelastic body takes into account the aging of the plate, but does not take into account longitudinal deformation. The stability research method is based on creation of a functional of Lyapunov type for the partial differential equations which satisfy aerohydrodynamic functions and deformations of plate. Sufficient stability conditions of the motion of an elastic plate imposing restrictions for parameters of mechanical system are obtained.
CYBERNETICS AND PHYSICS, Vol. 6, No. 4, pp.269-277