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An Effective Stiffness Theory for Elastic Wave Propagation in Filamentary Composite Materials.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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An approximate first order theory for elastic wave propagation in composite materials composed of long fibers of rectangular cross section embedded in a soft matrix is developed. Stress and displacement equations of motion, boundary conditions, and constitutive relations are included. Higher order stresses are related to average conventional stresses and moments of stresses. The boundary conditions are shown to be averaged forms of Cauchys law of classical elasticity. Procedures for reducing the theory to that of classical elasticity and that for laminates are established. Displacement equations of motion for a limited second order theory for flexural motion are presented. For propagation parallel to the fiber orientation in an unbounded medium, the motion separates into three distinct types LONGITUDINAL, FLEXURAL, AND TORSIONAL. All motions are dispersive and are sensitive to changes in relative material stiffnesses and geometry. For propagation perpendicular to the fiber orientation, the motion is dispersive and frequency spectra show stopping bands typical of periodic media. The propagation of plane waves parallel and perpendicular to the fiber orientation in an infinite plate is investigated for the case of plane strain. Resulting spectra strongly resemble those of homogeneous isotropic plates and show the same general sensitivity to material parameters as the infinite body results. Author-PL
APPROVED FOR PUBLIC RELEASE