Transverse vibrations of beam with localized heterogeneities

The formulation technique for the asymptotically exact coupling conditions simulating a thin section under the analysis of transverse vibrations of the cantilever fitted rod is presented. The three-piece beam model with constant characteristics in every area is investigated. An exact analytical solution produced from decisions of every interval associated with each other through the boundary conditions and matching conditions is obtained. Then, the analogous problem for the two-element beam model, for which asymptotically exact conditions on the coupling line of the uniform sections are formulated, is studied. The case of the vanishingly small thin cut is considered. The accuracy analysis of the obtained modified coupling conditions on the amplitude-frequency dependences and resonant frequencies is made. The residual values of the obtained conditions at various amounts of the cut length, depth, and central point are presented in the conducted computational experiments.