hr. J. Solids Smucrures. 1972, Vol. 8, pp. 1389 to 1405. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG Pergamon Press. Printed in Great Brrtain ELASTIC WAVE PROPAGATION IN FILAMENTARY COMPOSITE MATERIALS-f RODNEYA.BARTHOLOMEW$ Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio 45433 and PETER J. TORVIK~ Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433 Abstract-An approximate first order theory for elastic wave propagation in unidirectional, filamentary composite materials is developed. Included are stress equations of motion, boundary conditions and constitutive relations. For waves propagating parallel to the fiber orientation in an extended medium, the motion separates into three distinct types : longitudinal, flexural and torsional. All motions are dispersive and sensitive to changes in relative material stiffnesses and geometry, For propagation perpendicular to the fiber orientation, the motion is dispersive and the frequency spectra show stopping bands typical of periodic media. zyxwvutsrqponmlkjihgfedcbaZYXW 1. INTRODUCTION zyxwvutsrqponmlkjihgfedcbaZYXWVUTS IN ADDITION to their high strength over extended temperature ranges modern engineering composites possess properties which are potentially important as pulse-attenuation mechanisms. Among these, geometric dispersion, resulting from the interaction of the stress wave with the constituents, can make a significant contribution to the total dispersive nature of the material. The so-called “effective modulus” theories, which adequately describe the static behavior of composites, have been shown to be inadequate for describing the dispersive character of laminated composites [l]. As a result, much recent effort has been directed towards the development of improved theories to describe the dynamic response of these materials. One of the most active of these programs has resulted in the “effective stiffness theory” [l-9], which has been used extensively for analyzing the gross response of periodically laminated composites. The success of these studies suggests that the same basic approach can be used to describe the dynamic response of unidirectional filamentary composites as well. These materials, consisting of long stiff fibers deliberately oriented in a single direction and embedded in a softer matrix, serve as the basic building blocks of many laminated composites. In an early paper [3], Achenbach and Herrmann used the effective stiffness theory approach to describe an extended filamentary composite. They found that for waves t The material reported herein is based on a dissertation submitted by the first author in partial fulfillment of the requirements for the Doctor of Philosophy degree at the Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio. 1 Aerospace Engineer. 9:Associate Professor of Mechanics. 1389