Session: FSI-02-01 Flow-induced Vibration I

Paper Number: 62932

Start Time: Tuesday, July 13, 2021, 05:00 PM

62932 - Flutter of Rectangular Plate at Non-Zero Flow Yaw Angle 

Panel flutter is a phenomenon of self-exciting vibrations of skin panels of flight vehicles moving at high speeds. Usually panel flutter does not lead to immediate destruction of the aircraft, but results in the accumulation of fatigue damage of panels and the decrease of their lifetime. There are two types of panel flutter. The first one is the coupled-mode flutter, it is due to the interaction of two oscillation eigenmodes. The second type is the single-mode flutter, in this case the coalescence of eigenfrequencies and a significant change in the oscillation form do not take place. The single-mode flutter arises at a low supersonic speed.

The stability of the infinite series of thin elastic rectangular plates simply supported along all edges is investigated. Due to connections between spans, they are all either simultaneously stable or unstable. One side of the plate surface is exposed to a homogeneous supersonic flow of perfect inviscid gas. The other side experiences constant pressure so that the undisturbed state of the plate is flat. The boundary layer is neglected. The flow is adiabatic. The non-zero flow yaw angle is considered. The case of a supersonic leading edge is studied.

We use potential flow theory to derive expression for the unsteady aerodynamic pressure distribution over the oscillating plate. The plate motion equation, after the substitution of expression for unsteady aerodynamic pressure, with simply supported boundary conditions, is an integro-differential eigenvalue problem for finding complex eigenvalues. We use the Bubnov–Galerkin procedure for finding eigenvalues of the problem. The plate deflection is expressed as a superposition of basic functions, namely, mode shapes of the plate in vacuum. After substituting this expression into the equation of motion of the plate, we obtain a homogeneous system of linear algebraic equations for the coefficients in the expansion of the plate deflection. Equating the determinant of this system of equations to zero, we obtain the frequency equation. For the numerical solution of the frequency equation the iterative procedure is used. The flutter criterion is the sign of imaginary part of eigenvalue.

First, the convergence was studied and numerical parameters for flutter boundaries calculation were chosen. Next, flutter boundaries for the first eigenfrequencies were computed. Plates with different length and width were considered. Different values of flow yaw angle were investigated. Investigation has been conducted at Mach numbers from 1.1 to 1.7. All calculations were conducted for parameters, which correspond to a steel plate in an air flow at the altitude 3000 m above sea level. We obtained the values of the length and width of the plate and the angle at which single-mode and coupled type of panel flutter or stability occurs.

Presenting Author: Farrukh Abdukhakimov Lomonosov Moscow State University

Authors:

Farrukh Abdukhakimov Lomonosov Moscow State University
Vasily Vedeneev Lomonosov Moscow State University