Dynamic instability of shallow shells in three-dimensional incompressible inviscid potential flow

The system of the hypersingular integral equations with respect to the aerodynamic derivatives of the shell pressure drop is obtained to analyze the interaction of the shallow shell with three-dimensional incompressible potential air flow. This system of the integral equations is very applicable to analyze aeroelastic vibrations of thin-walled structures. The numerical approach based on the discrete vortices method is suggested to solve the system of the hypersingular integral equations. Using the assumed-mode method, the finite degrees of freedom dynamical system is derived to analyze the shallow shell dynamic instability. The dynamic instability of the shallow shell equilibrium in the subsonic air flow is analyzed numerically. This type of instability results in flutter. The influence of the structure parameters on the dynamic instability is analyzed. The parameters of the dynamic instability are compared with the data, which are calculated by the software ANSYS.