Interaction of shallow shell with subcritical potential stream
The system of singular integral equations with respect to aerodynamic derivatives is derived to analyze the in- teraction of the vibrating plate with subcritical gas stream. The pressure and velocity potential satisfy the Ber- noulli equation. The velocity potential and pressure are presented in the form of linear functions with respect to the generalized coordinates and the generalized velocity. The aerodynamic derivatives meets the Laplas equa- tion. Discrete vortex method is used to solve the system of singular integral equations. Using this method, the system of singular equations is transformed into the large dimension system of linear algebraic equations. The system of ordinary differential equations is derived by assumedmode method to describe the vibrations of shal- low shells. The frequencies of the selfsustained oscillations are compared with the eigenfrequencies to choose the eigenmodes, which are accounted in the expansions of the displacements. The characteristic exponents are calculated to analyze the shell dynamic instability. The influence of the shallow shell curvature and frequency of self-sustained oscillations on the parameters of dynamic instability is analyzed numerically.