a = distance from propeller to engine attachment, m Bhh = modal damping matrix cmq = aerodynamic derivative (pitching moment due to pitching) cm = aerodynamic derivative (pitching moment due to yaw angle) cnr = aerodynamic derivative (yawing moment due to yawing) cn = aerodynamic derivative (yawing moment due to pitch angle) cyq = aerodynamic derivative (side force due to pitching) cy = aerodynamic derivative (side force due to pitch angle) cy = aerodynamic derivative (side force due to yaw angle) czr = aerodynamic derivative (vertical force due to yawing) cz = aerodynamic derivative (vertical force due to pitch angle) cz = aerodynamic derivative (vertical force due to yaw angle) D = structural damping matrix D = aerodynamic damping matrix DP = propeller diameter, m FP = propeller disc area, m 2 fFL = flutter frequency, Hz fH = natural frequency of engine’s lateral vibrations, Hz fHdnws = natural frequency of engine’s lateral vibrations including downwash effect, Hz fV = natural frequency of engine’s vertical vibrations, Hz fVdnws = natural frequency of engine’s vertical vibrations including downwash effect, Hz f0 = natural frequency (in general), Hz G = gyroscopic matrix g = total artificial damping of vibrating system H = flight altitude, m HISA = flight altitude according to the International Standard Atmosphere, m Im = imaginary part Jx = mass moment of inertia about x axis, kg m Jy = mass moment of inertia about y axis, kg m Jz = mass moment of inertia about z axis, kg m j = imaginary unit K = structural stiffness matrix K = aerodynamic stiffness matrix KH = rotational stiffness of engine attachment in yaw (used for optimization), N m=rad Khh = modal stiffness matrix KV = rotational stiffness of engine attachment in pitch (used for optimization), N m=rad K = rotational stiffness of engine attachment in pitch, N m=rad K = rotational stiffness of engine attachment in yaw, N m=rad k = reduced frequency M = mass matrix MD = design maximum Mach number Mhh = modal mass matrix MY;P = aerodynamic moment around lateral axis—in propeller disc plane, N m MZ;P = aerodynamic moment around vertical axis—in propeller disc plane, N m mFUEL = fuel loading, % PY = propeller aerodynamic force in lateral direction at propeller disc plane, N PZ = propeller aerodynamic force in vertical direction at propeller disc plane, N p = eigenvalue Qhh = complex aerodynamic matrix q1 = flow dynamic pressure, Pa R = propeller diameter, m Re = real part t = time, s VD = design maximum speed, m s 1 VFL = flutter speed, m s 1 VTAS = flight speed (true airspeed), m s 1 V1 = flight speed, m s 1 w1 = downwash in vertical plane induced by aerodynamic forces, m s 1 w2 = downwash in horizontal plane induced by aerodynamic forces, m s 1 X = deflected x axis of propeller rotation x = undeflected x axis, x-direction distance, m ~ x = intermediate axis xi = design variable Y = deflected y axis y = undeflected y axis, y-direction distance, m Z = deflected z axis Received 2 February 2011; revision received 28 February 2012; accepted for publication 8May 2012. Copyright © 2012 byAeronautical Research and Test Institute, Prague. Published by theAmerican Institute ofAeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/12 and $10.00 in correspondence with the CCC. Senior Scientist, Strength of Structures Department, Beranovych 130. Associate Fellow AIAA. JOURNAL OF AIRCRAFT Vol. 49, No. 6, November–December 2012