Longitudinal acoustic mode in polymers. II. Solution of the general composite perturbed elastic rod

The theory of the longitudinal vibrations of a composite rod with perturbing forces at the ends has been generalized by the inclusion of inertial effects at the ends of the rod. The frequencies have been calculated for both symmetric and asymmetric forces and masses. The problem of coupled rods has also been treated, and its relation to the isolated rod is shown. These results should be applicable to the study of longitudinal acoustic modes in long chain molecular systems.