JOURNAL OF AIRCRAFT Vol. 41, No. 6, November–December 2004 Aeroelastic Modeling of Trailing-Edge-Flap Helicopter Rotors Including Actuator Dynamics Jinwei Shen ∗ and Inderjit Chopra † University of Maryland, College Park, Maryland 20742 The effect of actuator dynamics on a helicopter rotor with trailing-edge flaps for vibration control is investigated. Trailing-edge flap, actuator, and elastic rotor blade equations of motion are formulated using Hamilton’s variational principle. The coupled nonlinear, periodic equations are solved using finite elements in space and time. The baseline correlation study is based on wind-tunnel test data for a typical five-bladed bearingless rotor system. Good agreement is seen for the blade flap bending, chord bending, and torsion moments. It is shown that actuator dynamics cannot be neglected for a trailing-edge flap system with torsionally soft actuators. The parametric study performed using both coupled flap/actuator model and prescribed flap motion model indicated that the placement of trailing-edge flaps at 78% radius resulted in minimum flap input for this rotor. The vibration reduction level and trend are close between the predictions of both models at different forward speeds. Control inputs predicted by the coupled model show less sensitivity to the forward speed than that of prescribed model. Nomenclature a = lift curve slope C h = flap hinge moment coefficient c = blade chord c a = actuator torsional damping d = offset of flap hinge from blade elastic axis e = flap leading-edge location aft of midchord, in semichords F x = N b /rev longitudinal vibratory hub shear F y = N b /rev lateral vibratory hub shear F z = N b /rev vertical vibratory hub shear H = flap hinge moment (positive flap down) I f = flap second mass moment of inertia about flap hinge,  y f 2 dm J = scalar nondimensional vibration objective function k a = actuator torsional stiffness l = offset of flap hinge from flap leading edge l f = flap length M x = N b /rev roll vibratory hub moment M y = N b /rev pitch vibratory hub moment S f = flap first mass moment of inertia about flap hinge,  y f dm T = kinetic energy T 1−29 = Theodorsen flap constants U = strain energy U p = downwash velocity U t = air velocity tangential to blade chord u = blade elastic axial displacements v = blade elastic lag displacements W = virtual work w = blade elastic flap displacements x = blade spanwise position Presented as Paper 2000-1622 at the AIAA/ASME/ASCE/AHS 41st Structures, Structural Dynamics, and Materials Conference, Anaheim, CA, 6 April 2000; received 26 July 2002; revision received 15 January 2004; ac- cepted for publication 16 January 2004. Copyright c  2004 by Jinwei Shen and Inderjit Chopra. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/04 $10.00 in correspondence with the CCC. ∗ Graduate Research Assistant, Alfred Gessow Rotorcraft Center, Depart- ment of Aerospace Engineering. Member AIAA. † Alfred Gessow Professor and Director, Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering. Fellow AIAA. α = angle of attack β p = blade precone angle γ = lock number L = flap incremental lift (positive up) M = flap incremental pitching moment (positive airfoil leading edge up) δ = variation δ a = actuator input (positive flap down) δ f = flap deflection (positive flap down) θ 0 = rigid pitch angle ξ = blade modal response ˆ φ = blade elastic twist ψ = azimuth angle Subscripts a = actuator b = blade D = deformed blade coordinate F = trailing-edge flap coordinate f = trailing-edge flap H = trailing-edge flap hinge coordinate Superscripts ′ = d /dx ⋆ = d /d ψ ⋆⋆ = d 2 /d ψ 2 Introduction H ELICOPTER rotors are susceptible to high vibrations, because flexible rotor blades operating in an unsteady aerodynamic environment result in complex aeroelastic couplings. Higher har- monic control (HHC) and individual blade control (IBC) have been shown to be effective in minimizing vibration but at a considerable weight penalty and system complexity. 1 In HHC and IBC systems, blades are feathered at higher harmonics of rotational speed, gener- ating new unsteady airloads that if properly phased can cancel some of the original vibratory loads. Recently, with the emergence of smart material actuators, there have been growing activities to min- imize vibration actively with trailing-edge flaps. Such a control sys- tem is expected to be a compact, lightweight, low-actuation-power, and high-bandwidth device that can be used for multifunctional roles such as vibration and noise suppression, 2 aeromechanical stability improvement, 3,4 rotor performance enhancement, 5,6 and swashplateless primary rotor control. 7 A variety of comprehen- sive rotorcraft analyses 8−10 have examined the performance of 1465