Structural analysis for designing rotor blades with integral actuators

INTRODUCTION This paper presents an asymptotical formulation for analyzing multi-cell composite helicopter rotor blades with integral anisotropic active plies. It represents the first 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 cross section, 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 fiber composites distributed along the cross section of the blade. The formulation provides expressions for the asymptoticallycorrect cross-sectional stiffness constants in closed form, facilitating design-trend studies. These stiffness constants are then used in a beam finite 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 finite rotations, and now taking into account the presence of distributed actuators. Subject to external loads, active ply induced strains, and specific boundary conditions, the onedimensional (beam) problem can be solved for displacements, rotations, and strains of the reference line. Theoretical results are compared with experimental and other analytical results. * Boeing Assistant Professor, Department of Aeronautics and Astronautics. Senior Member, AIAA. Member, AHS. ^Graduate Research Assistant, Department of Aeronautics and Astronautics. Member, AHS Copyright©1998 by Carlos E. S. Cesnik and Sangjoon Shin. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. The technology of smart structures provides a new degree of design flexibility for advanced composite helicopter rotor blades [1]. The key to the technology is the ability to allow the structure to sense and react in a desired fashion, improving rotor blade performance in the areas of structural vibration, acoustic signature, and aeroelastic stability. There have been several approaches in the literature to take advantage of active materials for individual blade control [2, 3]. The one of interest for the proposed work is the integral actuation through the use of active fiber composites with interdigitated electrodes [4]. This actuator concept provides a feasible way of integrally actuating a rotor blade instead of the direct use of piezoceramic crystals. The latter was studied by Chen and Chopra [5, 6], following up on the work of [7], in a 6-ft diameter 2-blade Proud-scale rotor model with banks of piezoceramic crystal elements in ±45° embedded in the upper and lower surfaces of the test blade. There have been improvements in the actuation levels by using duallayer actuators and the maximum experimental tip twist actuation was of order 0.5°, still below the 1° to 2° necessary for the possible vibration control applications. On the other hand, the AFC concept obtains the level of authority needed for the actuation. Basic material characterization and proof of concept of an integral twisted-actuated rotor blade have been under investigation at MIT's Active Materials and Structures Laboratory [8, 9]. The objective of this paper is to present a methodology for analyzing advanced composite rotor blades with integral anisotropic active plies for designing of helicopter rotor blades. It supports the joint effort between the U.S. Army Vehicle TechnolAmerican Institute of Aeronautics and Astronautics Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. ogy Center, at NASA Langley Center, and MIT in designing model scale active twist rotor (ATR) blades for future wind tunnel testing in the Langley Transonic Dynamics Tunnel (TDT). The present analysis extends previous work done for modeling generically passive blades [10, 11, 12]. The approach is based on the two-step solution of the original three-dimensional blade representation by means of an asymptotical approximation: a linear two-dimensional cross-sectional analysis and a nonlinear one-dimensional global analysis [10]. The resulting model is expected to correctly predict the behavior of helicopter blades, accounting for the presence of different materials (passive and active) and an approximation of the actual blade shape. The cross-sectional analysis revises and extends the closed form solution of a thin-walled, multi-cell asymptotic formulation presented by Badir [13]. The variational-asymptotical method [14] is used to formulate the stiffness constants of a two-cell cross section with the active plies consisting of piezoelectric fibers. This cross-sectional analysis is a specialized case of the general framework established in [10]. It provides the expressions for the asymptoticallycorrect cross-sectional stiffness constants in closed form, facilitating design-trend studies. These stiffness constants will then be used in a beam finite element discretization of the blade reference line. The exact intrinsic equations for the one-dimensional analysis of rotating beams considering small strains and finite rotations developed by Hodges [11] and implemented by Shang and Hodges [15] is extended to take into account the changes in the constitutive relation. Subject to external loads, active ply induced strains, and specific boundary conditions, the onedimensional (beam) problem can be solved for displacements, rotations, and strains of the reference line. Finally, these results could be combined with information from the cross-sectional analysis in a set of recovering relations for stress/strain distribution at each ply of the blade. This structural representation will serve the basis for a future aeroelastic blade design model.