Remarks on stability of discrete-continuous structure under circulatory load

The paper deals with a problem of stability of a discrete-continuous structure under circulatory load. An example of the elastic column with localized loss of stiffness modeled as a flexible diminishing beam element is discussed in detail. Stabilization or destabilization of the system is observed, depending on localization and flexibility of a diminishing element. Continuous and discontinuous variations of the critical force are observed and thoroughly explained as a consequence of the mutual interaction of two kinds of characteristic curves, which were distinguished on the force-frequency plane. An analytical solution to the problem is found by the use of the transfer matrix method.