Flutter Analysis: Using Piecewise Quadratic Interpolation with Mode Tracking and Wind-Tunnel Tests

Abstract

= reference length of half-chord b j = breakpoint of the jth segment c 0 , c 1 , c 2 , c 3 , c 4 = coefficients of interpolation polynomial D = generalized damping matrix fV = cubic spline function of flow velocity f i = frequency corresponding to the flow velocity at the ith step g = added structural damping for k method Im = imaginary part of complex number j = sequence number of segment K = generalized stiffness matrix k = reduced frequency k j = the jth reduced frequency in which the generalized aerodynamic matrix is computed M = Mach number M = generalized mass matrix n = number of reduced frequencies for computing aerodynamic influence matrices n a = number of frequency data in a set p = Laplace variable Q s p = rational function approximation for generalized aerodynamic matrix Q 0 j , Q 1 j , Q 2 j = complex-valued coefficient matrices of the jth segment q = vector of generalized coordinates V = flow velocity V i = flow velocity at the ith step = flow density

Active flutter suppression of a multiple-actuated-wing wind tunnel model

“…10(b) also indicates that the frequency of the coupled bending-torsional mode is 6.36 Hz. Compared with previous wind tunnel tests for an open-loop system, 13 the critical flutter speed is lower, but similar to the prediction in Fig. 6.…”

“…More details about the finite element modeling of the MAW model can be found in the early work. 13 The comparison between the wind tunnel test of the initial MAW model and the numerical simulation of the corresponding finite element model showed strong discrepancies. In order to reduce the discrepancies, all gaps among the plastic foams in the MAW model have been filled with sponge, and the backlashes between the control surface and the wing have been plastered with tinfoil and rubber membrane.…”

Designing active flutter suppression for high-dimensional aeroelastic systems involving a control delay

“…The detail properties of the MAW can be found in Huang et al (2010). In the following numerical simulations, the initial values of the state variables of the aeroelastic system are chosen to be zero.…”

“…In this study, the first four elastic modes of the MAW (Huang et al, 2010) are used to establish the aeroelastic equation of motion. It is easy to establish the aeroelastic equation of motion in modal space according to Lagrange's equation and derive a set of linearized differential equations of motion as follows:…”

Single-Input/Single-Output Adaptive Flutter Suppression of a Three-Dimensional Aeroelastic System

“…The TEO control surface was connected to the wing by hinge-line mounting and can be driven by an EC-max 16 servo motor for flutter suppression. Detailed dimensions of the aeroelastic wind-tunnel model can be found in [11].…”