On dynamic stability of a nonlinear aeroelastic system

A nonlinear mathematical model of a device related to vibratory technology is considered. The device is intended for the intensification of technological processes, for example, the mixing process. The action of such devices is based on the vibrations of the elastic elements when they are flowed by the flow of the mixing medium. The dynamical stability of $ n $ elastic elements located inside the flow channel is studied. The subsonic flow of the gas-liquid medium (in the model of an ideal compressible medium) is considered. The definition of the stability of an elastic body corresponds to the concept of the stability of dynamical systems by Lyapunov. The model is described by a coupled nonlinear system of partial differential equations for unknown functions — the velocity potential of a gas-liquid medium and deformations of elastic elements. On the basis of the construction of the functional, the sufficient conditions for dynamic stability are obtained. The conditions impose restrictions on the flow velocity of the gas-liquid medium, flexural rigidity of elastic elements, and other parameters of the mechanical system.