ASYMPTOTIC AND NUMERICAL ANALYSIS OF COUPLED TIMOSHENKO BEAMS WITH DISSIPATIVE JOINTS

摘要

There are four standard types of dissipative linear joints for the problem of coupled beams; these are referred to as Types I-IV. In a previous publication, the author has performed an asymptotic analysis of the vibration spectrum for the case of two identical Timoshenko beams, coupled via a Type I joint and subject to energy conserving conditions at the ends. There it was found that the spectrum is a typical two-branched Timoshenko spectrum, except that, for most combinations of end conditions, at least one of the branches decomposes into two sub-branches, one damped and one undamped. Here, we generalize that treatment to all four joint types. In each case, we compute the vibration spectrum asymptotically, and we see that the spectral results for Types II-IV behave similarly to those for Type I. In addition, for some pairs of end conditions, all four joint types are equivalent, asymptotically, while for some other pairs of end conditions, the joint types are equivalent in pairs. We conclude with numerical results, via the Legendre-tau method, that confirm this asymptotic equivalence.