Mathematical modeling of some aerohydroelastic systems

The dynamics and stability of elastic elements of some aerohydroelastic systems – vibration devices designed to intensify of the technological processes, for example, for stirring gas-liquid media are investigated. The device is simulated by a flow channel containing elastic elements – deformable plates of variable thickness made from inhomogeneous material. A stream of a compressible or incompressible stirred medium (gas or liquid) flows inside the channel. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body, and linear models of the mechanics of liquid and gas are used. Models of vibration devices with different number and arrangement of elastic elements are considered. On the basis of the constructed functionals for the systems of partial differential equations, the sufficient stability conditions are obtained. The conditions impose restrictions on the parameters of mechanical systems.