A micromechanics and structural dynamics analysis of inherent damping exhibited by representative hybrid nanocomposite beams under axial strains is presented. The approximate model is used to assess, for the first time, the potential aeroelastic/aeromechanical stability enhancement of helicopter rotor blades from carbon nanotube matrix inclusions. The matrix/nano-inclusion micromechanics before interfacial slip occurs are based on the Cox model for discontinuous fiber reinforcement, and the frictional energy dissipation is assumed to be proportional to the interfacial shear force where slip has occurred. The validity of the model is established by comparing with experimental measurements of storage and loss moduli for a polymer nanocomposite. The relatively simple model captures the salient features of nanocomposite interfacial slip energy dissipation once uncertainties in fiber orientation and dispersement are accounted for by using an effective volume fraction. The validated model is then used to calculate damping of the first in-plane bending mode when a beam is subjected to axial strain fields that are representative of hingeless rotor blades. Results indicate that hybrid nanocomposites with nano-inclusions show significant potential for contributing to future vertical lift capabilities by augmenting rotorcraft aeromechanical stability margins of hingeless/bearingless rotors.
NomenclatureA BB Box beam cross-sectional area A s Interfacial surface area of fiber inclusion A NI , A RVE Cross-sectional area of nano-inclusion and RVE C xx Composite storage modulus c Representative rotor blade chord length d NI , r NI Nano-inclusion diameter and radius d RVE Diameter of representative volume element E NI , E M Carbon nano-inclusion and matrix longitudinal moduli EI z Beam in-plane bending stiffness f Interfacial shear force over the slipped portion of the matrix/nano-inclusion interface G M Matrix shear modulus h Box-beam height K M , K NI Equivalent lumped element axial stiffnesses of the matrix and nano-inclusions l Nano-inclusion length l Interface length over which interfacial slip occurs m Micromechanics model input parameter governing stiffness degradation after interfacial slip m 0 Beam cross-sectional mass per unit length * Research Aerospace Engineer, Vehicle Technology Directorate. Senior Member AIAA † Research Mechanical Engineer, Vehicle Technology Directorate. ‡ Research Mechanical Engineer, Vehicle Technology Directorate. § Research Aerospace Engineer, Vehicle Technology Directorate.