A perturbation technique described previously is applied to find the dispersion of free longitudinal waves in a long orthotropic bar of rectangular cross section as far as the fourth order of approximation. First the second‐order equations of motion and equations of compatibility are solved to find the second‐order stress distributions; then these are used to derive the exact second‐ and fourth‐order dispersion terms. The second‐ order stresses are related to a homogeneous and a nonhomogeneous potential function. The homogeneous potential function may be described by one of three analytical expressions, depending upon whether the following combination of elastic compliances is less than, greater than, or equal to unity:
A = (s11s33−s13 2) (s22s33−s23 2) / [(s12s33−s13s23) +(1/2) s33s66]2.
Measurements of the first two frequencies of two potassium chloride specimens, having different major orientations, are compared with theoretical predictions; the percent differences are 0.06%, 0.12%, 0.07%, and <0.01%, all of which lie well within the bounds permitted by the uncertainties in the governing parameters.
Subject Classification: 40.22, 40.20; 20.15.