Pochhammer Amplitude Distributions in an Infinitely Long Cylinder
In 1876, Pochhammer originally developed the equations for wave propogation in an infinitely long elastic cylinder with isotropic material properties. (Note: the Pochhammer solution is sometimes called the Pochhammer-Chree solution or the Pochhammer-Love solution.)
The following has been taken essentially from Zemanek's (1) analysis.
Axial amplitude distribution
For a cylinder of radius R, the axial amplitude Ua at a radial distance r from the center of the cylinder is given by equation 1. (See Zemanek (1), p. 271, lower equation 18.)
| 1) Ua(r) | = | 2 (γ R)² - Ω² | J1(k R) J0(h r) + | 2 (k R) (h R) J1(h R) J0(k r) |
where:
| 1a) γ | = | 2π f |
| C |
| 1b) Ω | = | 2π f R |
| Cs |
