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

Abstract

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.

On the influence of boundary conditions on the dependence amplitude-frequency of non-linear flutter type oscillations of rectangular plate at critical speed.

“… and 2  -are first and second natural frequencies of the plate, while  is the reduced speed parameter. The solution of the nonlinear problem is usually preceded by analysis of the corresponding linear problem, which is done in detail in the work [6] and accordingly, the critical flutter speed in the case of the selected buckling form of the plate is obtained. After the nonlinear problem is solved using harmonic balace method.…”

“…After the nonlinear problem is solved using harmonic balace method. As a result the system of non-linear algebraic equations are obtained [6].…”

“…Brought in [4,5] Table 1 the symbol "-" means that the amplitude of oscillation for the specific parameter set is equals to zero and there are no periodic solutions of the system (15) of the work [6]. Figure 1 is plotted on the basis if the Table 1.…”

“…There are many investigations devoted to the study of stability of plates and shells in supersonic gas flow [1][2][3][4][5]. A short review of up-to-date known results is brought in the work [6]. Let us note here the results devoted to the present work only.…”