Flutter of elastic plate in air flow at small supersonic speed.

Fluid, gas and plasma mechanics


Аuthors

Shitov S. V.

State Moscow Plant «Salyut», 6, Plehanova str., Moscow, 111123, Russia

e-mail: SHLTOV@GMAIL.COM

Abstract

In the linear approximation, we investigate the stability of elastic thin metal strip that is mounted in an absolutely rigid surface. The band has a periodic hinge reinforcement, thus, the band consists of a series of identical spans, separate span will be called a plate. All the edges of the plate is set hinged support. We consider small oscillations of the plate, which are described by the equation of motion of the Kirchhoff-Lyave. Oscillation occurs adjacent plates in opposite phase.

The band is streamlined with one hand supersonic flow, and the other is set to a constant pressure, which balances the band in a flat undisturbed state. Feed gas flows steadily perpendicular to the front edge of the plate. Gas modeled nonviscous and perfect. Perturbations of the gas is sufficient to consider potential. In the linear approximation of the motion is described by the wave equation.

Unsteady nonviscous gas pressure acting on the oscillating plate obtained from gas dynamics, has the form of two-dimensional integral of a combination of deflection plate and its derivative, with a core of special functions [30]. This two-dimensional integral can be reduced to one-dimensional in the case of the strip, is a series of rectangular plates. Such a statement can be considered as a first approximation to the study of flutter isolated rectangular plate. Expression for the pressure in the limit of M → +∞ gives the formula piston theory, but at Mach 1 < M < 2 nothing to do with the piston theory is not, moreover, in this range, there is another type of flutter (singlemode), which is different from classical coupled mode flutter of plate. Single-mode flutter largely been studied in two-dimensional problem in [23], [24] and [25], [26], experiments were conducted confirming its presence. In this paper we study the three-dimensional setting.

Further, given the fact that the pressure is expressed through the deflection plate, get one closed integro-differential equation of oscillations of the plate. Thus, the problem of stability in the linear approximation is the problem of finding the complex natural frequencies of the equation. This problem is solved numerically by the Bubnov-Galerkin method. The system is unstable if and only if at least one of the natural frequencies has a positive imaginary component.

In conclusion, in the linear approximation, we consider the problem of the stability of elastic bands. To calculate the pressure acting on the deflection of the plate, use the exact theory of potential flow of gas. For the first four frequency domains of instability in the plane (Lx; M) for different values of Ly. Where Lx and Ly --- dimensionless length and width of the plate (physical length and width divided by the thickness of the plate), --- the Mach number of the incident flow.

Keywords:

panel flutter, flutter of plate, onemode flutter, flutter with one degree of freedom

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