Asymptotic analysis of the vibration spectrum of coupled Timoshenko beams with a dissipative joint

Complex flexible structures often are composed of simpler objects like beams joined end-to-end. We consider the case of two identical Timoshenko beams, coupled together at a typical energy-dissipating joint. The Wave Propagation Method of Keller and Rubinow is employed to compute the vibration spectrum of the system. It is found that the spectrum consists of a typical double-branched Timoshenko spectrum. In addition, however, for most combinations of energy-conserving end conditions, at least one of these branches decomposes into two sub-branches, one which is damped and one, undamped.