Influence of supersonic gas flow on the amplitude of non-linear oscillations of rectangular plates.

The problem of nonlinear oscillations of isotropic rectangular plate in supersonic gas flow is examined. The study was conducted taking into account both types of non-linearity: wind (quadratic and cubic) and geometric (cubic). Due to the aerodynamic nonlinearity (especially its non-symmetric quadratic part) it is established that dependence amplitude-speed is two-valued at the certain intervals of the speed. This fact is illustrated on the figures given in the text in the form of two branches, the lower branches of which, in all probability, are unstable. The unstable branches are separated via the gravitational field of two adjacent sustainable solutions. Thus the perturbation magnitude can be easily found, which is required in order to transfer the system from one stable branch to another. Existence of specific areas of the speed is shown in which undamped flutter type oscillations cannot be excited in both pre-critical speeds and in post-critical stage.