ABSTRACT
Prior to the advent of digital computers, the algebraic complexity of wave propagation problems necessitated lengthy and time-consuming hand calculations for accurate solutions. Accordingly, geometric means were developed for approximate calculations. The variation in acoustic properties with direction in anisotropic media can be represented geometrically in a variety of ways. These representations remain useful in illustrating various aspects of wave propagation in anisotropic media. R. Kriz and H. Ledbetter have extensively studied the use of representation surfaces to describe the mechanical behavior of fiber-reinforced structures. The directional dependence of elastic properties can be easily visualized with such techniques. The loci of the endpoints of all such vectors form a two-dimensional section of the elastic representation surface. By considering all possible directions, the entire three-dimensional surface can be developed in an analogous fashion. Note that the section for a zero fiber volume fraction is circular as the resin itself is isotropic.
