A simple formula for the longitudinal modes in a cylinder.
For CT<C<CL, the Pochhammer dispersion relation can be replaced by an approximate equation which can be solved to obtain the dimensionless wave number explicitly as a function of the phase velocity. This equation is similar to the corresponding equation for the Lamb modes in plate. The two types of modes are interlaced, i.e., between every pair of modes of the plate there is a longitudinal mode of cylinder and vice versa.
Ahmad
Faiz
F
Department of Mathematics, College of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. faizmath@hotmail.com