UNSTEADY AERODYNAMICS IN TIME AND FREQUENCY DOMAINS FOR FINITE-TIME ARBITRARY MOTION OF HELICOPTER ROTOR BLADES IN HOVER AND FORWARD FLIGHT (AEROELASTICITY, NONLINEAR PERIODIC SYSTEMS, CASCADE AERO, MODELING, RATIONAL APPROXIMATIONS)

Several incompressible finite-time arbitrary-motion airfoil theories suitable for coupled flap-lag-torsional aeroelastic analysis of helicopter rotors in hover and forward flight are derived. These theories include generalized Greenberg's theory, generalized Loewy's theory, and a staggered cascade theory. The generalized Greenberg's and staggered cascade theories were derived directly in Laplace domain considering the finite length of the wake and using operational methods. The load expressions are presented in the Laplace, frequency, and time domains. Approximate time domain loads for the various generalized theories are obtained by developing finite state models using Pade approximant of the appropriate lift deficiency functions. Three different methods for constructing Pade approximants of the lift deficiency functions were considered and the more flexible one was used. Pade approximants of Loewy's lift deficiency function, for various wake spacing and radial location parameters of a typical helicopter rotor blade section are presented.; In the second part of this study the influence of finite-state arbitrary-motion time-domain aerodynamics on rotor blade aeroelastic stability was illustrated for hover and forward flight conditions. The generalized Greenberg time-domain unsteady aerodynamics was incorporated in a nonlinear coupled flap-lag analysis of a hingeless rotor. Aeroelastic stability boundaries for both hover and forward flight are obtained using both arbitrary-motion time-domain aerodynamics and quasisteady aerodynamics. The sensitivity of flap-lag aeroelastic stability boundaries to time-domain arbitrary-motion unsteady aerodynamics is evaluated by comparing the two sets of results for various blade configurations and flight conditions. Mathematical solution techniques for dealing with a problem which combines arbitrary-motion unsteady aerodynamics with the nonlinear dynamic equations of blade equilibrium in forward flight, which have periodic coefficients, were illustrated.