Flutter of a Plate at High Supersonic Speeds

Abstract

The vibrations of plate structures placed in a supersonic flow was considered. The undisturbed fluid flow was parallel to the plate. This type of problem is especially important in the aerospace industry, where it is named panel flutter. It has been noticed for a long time that panel flutter may be problematic at high speeds. In this article, two specific problems were treated: in the first one, the plate was in the form of an infinite strip and the flow was in the direction of its finite length. Rigid walls indefinitely extended from the sides of the plate. In the second problem, the plate was a finite rectangle and the flow was parallel to one of its sides. The rest of the plane of the rectangle was again rigid. The first problem was a limiting case of the second problem. The flow was modeled by piston theory, which assumes that the fluid pressure on the plate is proportional to its local slope. This approximation is widely used at high speeds (supersonic speeds in the range of M > 1), and reduces the interaction between the fluid flow and the vibrations of the plate to an additional term in the vibration equation. The resulting problem can be solved by assumed mode methods. In this study, the solution was also found by using the collocation method. The contribution of this study is the correlation between the flutter velocity and the other parameters of the plate. The main result is the flutter velocity of the free fluid flow under which the plate vibrations become unstable. Finally, simple expressions are proposed between the various non-dimensional parameters that allows for the quick estimation of the flutter velocity. These simple expressions were deduced by least squares fits to the computed flutter velocities.

Keywords

• flutter velocity
• flow-induced plate vibration
• piston theory
• collocation method
• shooting method