Aeroelastic Tailoring of Composite Couplings and Blade Geometry of a Helicopter Rotor Using Optimization Methods Ranjan Ganguli* Indcrjit Chupra Assist<tt~t Reenx:lt Scientist Proj2!.s,sor rurd Directo, Alfred Gessotv Rvrorcrnfr Cer~ter Depnmoent of Aemspnce Etlgineeritlg U~liversity of M~t~~/aylo,rd, College Park, Mnrylntd An aeroelastic analysis based on a finite element method in space and time is developed for an advanced geometry conipmite rotor. Optimization studies am carried out for a fonr-bladed, soft-inplane hingeless mtor with variable sweep, anhedral and planform taper, and with a two-cell composite box-beam spar. The objective function includes vibratory hub loads and vihra- tory bending moments; constraints am imposed on blade mtating frequencies, aeroelastic stability and antorotational inertia. Design variables include ply angles of the laminated walls of the box-beam, sweep, anhedral and planform taper, and non- structural mass and its chordwiw offset from the elastic axis. Aerwlastic optimization is performed for different combinations of design variables. The starling design is a straight blade with no composite coupling. Compared to the starling design, an op- timized solution achieved a d u c t i o n in the 41ntv loads of 4-60 pemeut, and 15-25 percent in the peak-to-peak vibratory flap and lag bending moments. Notation Cd drag coeficient C, list coefficient C, pitching moment coeilicienl C, thrust coeilicient c blade chord clp planform taper D dcsign variables D. j - I, ... 11 J .- El,. blade flap bending st~Rncss El, blade lag knding liffness 41rev longitudinal huh force F${ 4Irev laterd hub force F;'; 41rev vertical hub force GJ blade torsional stiffness g constaints J objective function Ks svuctural stiffness m a h x - k blade composite couplings - b3 blade flap bcnding-torsion composite coupling - b4 blade lag knding-torsion compnsilc coupling MI svuctural mass matrix M${ 4Irev hub roll moment M 41rev huh pitch moment M:; 4Irev hub yaw momcnt Md steady hub yaw moment m,, nonstmctural mass nl, refcrcnce mass per unit length N number of spatial finite elements, number of blades R rotor radius Presented in pan at Ule American Helicopter Society 51sl Annual Forum, For! WorUI. I", May 9-1 1,1995. Manuscript submiltod Sept. 1995: accepted Feb 1997. *CurrenUy at GE Corporate R&D Lab. Schencclady, NY. kinclic energy, rotor thrust axial deformation of bladc strain energy lag dclormaliun of blade flap dcFormaliun of hlade virtual work normalized complex cigcnvector of transiti<lnni;~lrix blade geometry and inertial design variahlcs blade response chordwise olFsct of nunstmclural mass from elastic ;]xis (positive l o w a d ) angle of attack at bladc section real pan of charactcristic exponcnl of kth mode minimum acceptable level of damping lor MI1 mrlde ply angle dcsign variables eigcnvalue of kth stability mode sweep angle (positive forward) anhedral angle (positive upward) advance ratio solidity ratio torsional dcformaliun of blade mode shape azimuth anglc, time Floquet state Uansition matrix blade mtating ireqeqoencies rotation specd lag mode flap mode torsion mudc imaginary par( real pan lower bound upper hound