An asymptotic and numerical analysis of the vibration spectrum of two Timoshenko beams coupled by general linear dissipative joints

An asymptotic analysis, using the Wave Propagation Method of Keller and Rubinow, was performed on the problem of two identical Timoshenko beams coupled end to end via a so called Type I energy-dissipative joint in 2010. This paper generalizes those results by employing the same method to treat the problem involving any of the four standard types of dissipative joint. A numerical analysis also is performed, and a comparison of the results shows a good match, once one is far enough along the spectrum. In addition, it is found that numerical results for increasing values of the aspect ratio approach the corresponding Euler-Bernoulli beam results, and the asymptotically undamped Timoshenko modes are found to play a lesser role as the aspect ratio increases.