Vibration Analysis of Elastic Uniform Cantilever Rotor Blades in Unsteady Aerodynamics Modeling

Abstract

A = blade cross-sectional area equations, m a = lift-curve slope, 2 =rad b = number of blades C = blade chord, m [c] = modal damping matrix C k = Theodorsen’s function Cd0 = drag coefficient D = profile drag per unit length, N=m E = Young’s modulus, N=m G = Shear modulus, N=m h = vertical displacement normal to freestream velocity component V, m I2, I1 = cross-sectional area moments of inertia about the y0 and z0 axes, respectively, m J = torsional stiffness constant, m KA = polar radius of gyration, m Km = mass radius of gyration, m [k] = modal stiffness matrix L = lift per unit length, N=m Lu, Lv, Lw = aerodynamic forces per unit length M = moment per unit length, N m=m [M] = modal mass matrix M = moment per unit length, N m=m m = mass per unit length, kg=m R = blade length, m R = flap-lag structural coupling parameter T = aerodynamic force per unit length, normal to blade airfoil chord line, N=m U = airfoil velocity with respect to fluid, m=s u, v, w = elastic axis displacements in x; y; z , m Vi = induced flow velocity X, Y, Z = unreformed coordination system, m x = dimensionless length, x=R = airfoil section angle of attack, radian