Longitudinal vibrations of a double-rod system coupled by springs and dampers

A method of obtaining the exact solution for the forced vibrations of elastic rods coupled by distributed springs and dampers was presented. The method was based on the change of variables to decouple the set of two second order partial differential equations, and then the solutions were obtained by means of modal analysis. The two restrictions of this method were that the rods must be identical, and the boundary conditions on the same side of the system must be the same. It was found that the method provides an analytical solution that can serve as a benchmark for further investigation of more complex n-rod systems.