On the determination of the elastic moduli of anisotropic media from limited acoustical data

The determination of the elastic moduli of generally anisotropic media from acoustic information has a long history. It is known that, given measurements of the three wave speeds and corresponding polarization vectors in various directions n̂∈R3, all 21 elastic moduli can be determined [A. N. Norris, Q. J. Mech. Appl. Math. 42, 413 (1989)]. However, in some practical cases, depending upon the type of loading a structure will see, not all 21 elastic moduli are needed, and it is therefore of interest to know how many of the constants can be determined from a less robust data set. In this paper, upper bounds are placed on the number of elastic constants that can be determined from acoustic data, which is limited to one or two planes. It is shown that for generally anisotropic media, 15 elastic constants can be uniquely obtained from data taken in one plane, and 20 of the 21 elastic constants can be uniquely obtained from data taken in two planes. Specific examples are given to illustrate the general results.