Bifurcation diagrams and stability boundaries of circulatory systems

Stability problems of linear circulatory systems of general type with finite degrees of freedom depending on two parameters are considered. It is shown that these systems in the generic case are subjected to flutter and divergence instabilities. Bifurcations of eigenvalues describing mechanism of static and dynamic losses of stability are studied, and geometric interpretation of these catastrophes is given. For two-dimensional case boundaries between stability, flutter and divergence domain and generic singularities of these boundaries are analyzed. With the use of the left and right eigenvectors and associated vectors tangent cones and normal vectors to the boundaries are calculated. As an example stability of a rigid panel vibrating in airflow is considered and discussed in detail.