AEROELASTIC RESPONSE OF NONLINEAR WING SECTION BY FUNCTIONAL SERIES TECHNIQUE

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indiciai functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcriticai aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied. Nomenclature a Dimensionless elastic axis position measured from the mid-chord, positive aft c Chord length of 2-D lifting surface, 2b Ch_,C_, Kh_, K_ Damping and stiffness coefficients in plunging and pitching (i=1,2.3 linear, quadratic, cubic), respectively CL,_ Lift-curve slope C(k _ F(k), G(k) Theodorsen's function and its real and imaginary counterparts, respectively h,_ Plunging displacement and its dimensionless counterpart, (h/b), respectively h, H. n-th order Volterra kernel in time, and its Laplace transformed counterpart, respectively I,_, r_ Mass moment of inertia per unit wingspan and the dimensionless radius of gyration, (I s/mb 21/2 , respectively la,m _ Dimensionless aerodynamic lift and moment, (L,b/mU2)and (Mb'/I_U_), respectively L, M. Total lift and moment per unit span Lb, lb Overpressure signature of the N-wave shock pulse and its dimensionless counterpart, (Lbb/mU _ ), respectively m,/1 Airfoil mass per unit length and reduced mass ratio, (rn/rcpb 2 ), respectively N Load factor, 1 + h'/g , p 2 Pm _o Peak reflected pressure amplitude and its dimensionless counterpart, ( mb/mU_ ), respectively r Shock pulse length factor s j, _' Laplace transform variable and Laplace operator, respectively, sj = ikj;i2 = -1 S,_, Z_ Static unbalance about the elastic axis and its dimensionless counterpart, S_ rob, respectively t, %, z Time variables and dimensionless counterpart, (U.t/b), respectively tp,z e Positive phase duration, measured from the time of the arrival of the pulse, and its dimensionless value, respectively TF Transfer function Uoo, V Freestream speed and its dimensionless counterpart, (U=/bco_ ) x(t) Time-dependent external pulse (traveling gusts and wake blast waves) y(t) Response of the considered degree of freedom (pitch o_and/or plunge h) a Twist angle about the pitch axis (h, _',_ Structural damping ratios in plunging (ch/2mco,,), and pitching (c,_/2I,_o9,_), respectively p Air density _('t') Wagner's indicial function to, k Circular and reduced frequencies, (a_b / U= ), respectively cob,co _ Uncoupled frequencies in plunging and pitching, (Kh/m) _'2 and (K_/I_)1/2, respectively Plunging-pitching frequency ratio, (coh/co d )