Nonlinear aeroelastic oscillations in the wall of a flat channel filled with viscous gas and resting on a vibrating foundation

This article considers the problem of aeroelastic oscillations in the channel wall having a suspension with hardening cubic nonlinearity, which were induced by the vibration of the channel foundation. The narrow flat channel formed by two parallel rigid walls and filled with pulsating viscous gas was examined. The bottom wall was stationary, while the opposite one had a nonlinear elastic suspension. The aeroelasticity problem was formulated for the isothermal state of the gas and channel walls. Considering the narrowness of the channel, the equations of dynamics were derived for a thin layer of the viscous gas, and the asymptotic analysis of the problem was performed by the perturbation method. Using the method of iterations, the law of viscous gas pressure distribution in the channel was determined, and the equation of aeroelastic oscillations in the channel wall was obtained as a generalization of the Duffing equation. This equation was solved by the harmonic balance method. The primary nonlinear aeroelastic response of the channel wall and the nonlinear phase shift were expressed as implicit functions. These characteristics were studied numerically to evaluate the influence of the nonlinear elastic suspension of the channel wall and the viscous gas inertia and compressibility on the nonlinear oscillations in the channel wall.