On the modeling of integrally actuated helicopter blades

This paper presents an asymptotical formulation for preliminary design of multi-cell composite helicopter rotor blades with integral anisotropic active plies. It represents the ®rst attempt in the literature to asymptotically analyze such active structure. The analysis is broken down in two parts: a linear two-dimensional analysis over the crosssection, and a geometrically non-linear (beam) analysis along the blade span. The cross-sectional analysis revises and extends a closed form solution for thin-walled, multi-cell beams based on the variational-asymptotical method, accounting for the presence of active ®ber composites distributed along the cross-section of the blade. The formulation provides expressions for the asymptotically correct cross-sectional sti€ness constants in closed form, facilitating designtrend studies. These sti€ness constants are then used in a beam ®nite element discretization of the blade reference line. This is an extension of the exact intrinsic equations for the one-dimensional analysis of rotating beams considering small strains and ®nite rotations, and now taking account of the presence of distributed actuators. Subject to external loads, active ply induced strains, and speci®c boundary conditions, the one-dimensional (beam) problem can be solved for displacements, rotations, and strains of the reference line. Analytical and numerical studies are presented to compare the proposed theory against the previously established analytical models. Discrepancies are found for general blade cross-section and discussed herein in details, especially for the piezoelectric actuation components. Direct results of the present formulation are also compared with experimental data