Mathematical modeling of some aeroelastic systems

In this paper, we develop mathematical models of a class of aerohydroelastic systems, namely, vibrating devices intended for intensification of technological processes. The dynamic stability of elastic components of these devices is examined. The notion of stability of a deformable body accepted in this paper coincides with the concept of the Lyapunov stability of dynamical systems. The models considered are governed by coupled nonlinear partial differential systems. The impact of a gas or fluid (in the model of an ideal medium) is determined from the asymptotic equations of aerohydromechanics. For describing the dynamics of elastic elements, we use the nonlinear theory of solid deformable bodies, which takes into account transverse and longitudinal deformations. The study of stability is based on the construction of positive-definite Lyapunov-type functionals. Sufficient conditions for the stability of solutions of the systems proposed are obtained.