Flutter Mechanism of Timoshenko Beams in Supersonic Flow

Abstract

The flutter mechanism for cantilevered beam in supersonic flow is studied based on Timoshenko beam model and piston theory. The partial differential equations governing transverse deflection and rotation angle of the beam are derived by analyzing the finite section of the beam. Based on the mode functions of the unperturbed system, complex natural frequencies are investigated to predict the instability of the beam by Galerkin truncation. The mechanism of both coupled-mode and single-mode flutter caused by the supersonic flow are spotted for different flow velocity with consideration of the shear deformation and rotary inertia in the beam structure by the analytical method. The instability region is discussed by Routh-Hurwitz criterion. The critical Mach number for the panel motion becoming unstable is calculated for given values of the dimensional parameters.