the offset between the centre of gravity of the rotor and the central line of the clean wing and its dimensionless counterpart, respectively u o , v 0 , w o displacements in the X, Y and Z directions of the beam centre-line, respectively x,y,z local co-ordinate system with origin coinciding with rotor's centre of gravity X,Y,Z global, inertial co-ordinate system with origin O at the wing root cross-sectionGreek symbols α(t) tilt angle (= Ω 2 t) of the pylon/nacelle with respect to the wing upper face δ variation operator ∆ Dirac delta function ρ mass-density θ ply-angle θ X , θ Y , φ rotations of the wing cross-section about the X, Y and Z axes, respectively Ω 1 , Ω 2 (Ω 1 , Ω 2 ) angular velocity of the rotor and of the pylon/nacelle, and their dimensionless counterparts, respectively
Sub/superscriptsB, R and E identify the affiliation of any quantity affected by these sub/superscripts to the wing, rotor, and the pylon/nacelle, respectively ABSTRACT Problems related with the mathematical modelling and eigenvibration of a tiltrotor aircraft-wing system built up of anisotropic composite materials are investigated. The wing-mounted rotor that can tilt from the vertical position to a horizontal one is modelled and analysed from the vibrational point of view. In this sense, its behaviour is analysed as a function of the mass size, mass moment of inertia, tilt angle and spin speed of the spinning rotor and of its location along the wing span. While the rotor is considered to be rigid, the aircraft wing is modelled as a thin-walled beam that features a doubly-symmetric cross-section contour and incorporates the elastic coupling between flap-lag-transverse shear, on one hand, and between extension-twist, on the other hand. Numerical simulations are provided and pertinent conclusions are outlined.
NOMENCLATUREhight, chord of the wing cross-section and its wall thickness, respectively J xx , J yyxx (≡ J yy + J zz ) rotor's mass moment of inertia about the x, y and z axes, respectively pylon/nacelle mass moment of inertia about the X, Y and Z axes, respectively L semi-wing span mass of rotor and of pylon/nacelle, and their dimensionless counterparts, respectively. m 1 L (= m w ) mass of the semi-wing p Y ≡ p Y (Z,t) transversal load THE AERONAUTICAL JOURNAL E E E XX YY ZZ J J J 1 , ( / ) R R R m m m m L = 1 ( / ) E E E m , m m m L = , ( / ) m m m r r r L =