Resonance of proper frequency 1:2 - reason for hard excitation oscillations for plate in ultrasonic gas flow
A well know problem of oscillations for plate in ultrasonic gas flow is considered. The mathematical model chosen is the boundary value problem proposed by V.V. Bolotin where
aerodynamic forces are accounted for on the basis of flat section law (piston theory). The linear and nonlinear version of the problem is considered with the damping coefficient assumed to be
small. It is shown that proper frequency 1:2 oscillation occurs for velocities significantly smaller than the velocity of flutter. In the nonlinear version this situation allows us to show that
there always exist unstable periodic solutions in a small neighbourhood about the equilibrium state. The latter comment implies that in the range up to critical velocities there is a
possibility of hard excitation oscillations which can result in the destruction of the construction. The analysis of the problem in the nonlinear setting is based on the direct application of the
normal form method to the nonlinear boundary value problem.