Mathematical Modeling of the Aeroelastic Response of a Disk Having a Nonlinear Elastic Suspension and Interacting with a Layer of Viscous Gas

Abstract

In this paper, a mathematical model of nonlinear aeroelastic oscillations of a disk that has a suspension with hardening cubic nonlinearity and interacts with a layer of viscous gas pulsating due to a specified disturbance on its contour is presented. An asymptotic analysis, which made it possible to reduce the initial model to the generalized Duffing equation, based on the solution of which the main aeroelastic response of the disk and its phase shift were found using the harmonic balance method, was carried out. The characteristics in particular cases provide a transition to an incompressible viscous fluid and a linear elastic suspension, while their numerical study made it possible to establish that the compressibility of the gas leads to an increase in the values of the resonant frequencies and an increase in the amplitudes of the disk oscillations. Calculations showed the possibility of suppressing unstable oscillations of the disk near resonant frequencies by changing the thickness of the gas layer. The obtained results can be used to study the dynamics of gas and liquid dampers and supports, as well as sensitive elastic elements of pressure sensors.