Review article

The paper studies parametric vibrations and dynamic stability of homogeneous and inhomogeneous (two-layered) toroidal shells interacting with an elastic medium. The above-ground and underground shells` positions are considered. The computational models correspond to curvilinear sections of trunk pipelines of 1020-1420 mm diameter for liquid or gas transportation. Pipelines are subjected to static and dynamic loads affecting their reliability. Dynamic impacts can be caused by the operation of pumping or compressor stations, seismic activity and other factors. Increase of pipelines resource is connected with elimination of harmful vibrations that lead to insulation failure, corrosion cracking and fatigue failure. In complex cases, accidents with economic and environmental consequences are possible. The aim of the study is investigation of parametric resonance and dynamic stability of shells in interaction with the environment. Based on the Mathieu equation and the Bogoliubov-Mitropolsky methodology, the boundaries of the dynamic instability are determined for different shell arrangements. Unsteady internal pressure, longitudinal compressive force and elastic ground base are taken into account.