Coupled Helicopter Rotor/Flexible Fuselage Aeroelastic Model for Control of Structural Response

Abstract

A re ned coupled rotor/ exible fuselage aeroelastic response model is developed for vibration reduction studies based on active control of structural response (ACSR). The structural model is capable of representing exible, hingeless rotors combined with a exible fuselage, and a rigid platform combined with the actuators required for modeling the ACSR system and is combined with a free wake model. The in uence of rotor/fuselage coupling and improved aerodynamics on the vibratory hub loads is investigated. Nomenclature A= beam cross-sectional area a NbC , a Nb S = cosine and sine parts of acceleration at various fuselage locations a z = fuselage vertical acceleration at various locations C d0 = blade drag coef cient C O , C I , C NW = matrices of induced velocity in uence coef cients C W = helicopter coef cient of weight c = blade chord D = wake distortion E = Young's modulus of elasticity E I y , E I z = blade bending stiffnesses in ap and lead-lag= blade aerodynamic, gravitational, and inertial forces F b0 , F bnc , F bns = Fourier coef cients of blade equations of motion F e0 , F enc , F ens = Fourier coef cients of elastic fuselage equations of motion F fus = total fuselage forces F NbC , F Nb S = cosine and sine parts of rotor hub forces F r0 , F rnc , F rns = Fourier coef cients of fuselage rigid body equations of motion F T , M T = tail rotor thrust and moment F x , F y , F z = vibratory hub shear components F 0 , M 0 = constant part of rotor hub loads f C d f = fuselage equivalent at plate drag area G J = blade torsional stiffness [I ] = fuselage inertia tensor I p = polar moment of inertia I x , I y , I z = fuselage beam cross-sectional principal moment of inertia J = beam torsional constant L = Lagrangian M = fuselage total mass M A b , M G b , M I b = blade aerodynamic, gravitational, and inertial moment M fus = total fuselage moments M Nb C , M Nb S = cosine and sine parts of hub moments M ns = nonstructural consistent mass matrix M x , M y , M z = vibratory hub moment components m b = blade mass distribution per unit length N = matrix of shape functions for calculation of nonstructural mass matrix N b = number of blades N H , N el , N rg = number of harmonics retained in Fourier expansion of blade, fuselage elastic, and rigid body degrees of freedom Q i = fuselage generalized force q = response vector q b , q e , q r = vectors of blade, fuselage elastic, and rigid body degrees of freedom q b0 , q bnc , q bns = Fourier coef cients of blade response q e0 , q enc , q ens = Fourier coef cients of fuselage elastic response q r0 , q rnc , q rns = Fourier coef cients of fuselage rigid body response R = rotor radius R x , R y , R z = fuselage rigid body translational degrees of freedom R 0 = fuselage center of mass position in inertial frame r b = position of rotor blade point r w = position of wake element r 0 = undeformed position of fuselage point with respect to the fuselage center of mass in fuselage reference frame r 0 = deformation of fuselage point in fuselage reference frame T = kinetic energy U e = e...

Nonlinear Rigid-Elastic Coupled Modeling and Oscillation Mechanism Analysis of Rotor-Body-Slung-Load System

“…The model considered the couplings of fuselage elastic deformations and rigid-body motions using a formulation based on the floating frame attached to an arbitrary material point. Cribbs [21] presented a model based on the mean axes floating frame, avoiding the arbitrary point selection, while Meirovitch [22] pointed out that mean axes were time-varied. To avoid the tedious task of expressing aerodynamic loads in the time-varying mean axes, a model based on quasi-coordinates was presented.…”