Simple accurate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using series expansion for axial coordinate and Fourier series for the circumferential direction, a simple explicit solution is obtained. Also, the influence of deformation component is investigated, it is shown that it can be neglected. Good agreement with experimental data and FEM is shown. The advantage of a current approach over the existing formulas is simplicity in programming.

Mine subsidence can pose a considerable threat to pipeline integrity. There are three constituents which quantitatively determine the distribution of strains along the pipelinethe function of ground displacement along the pipeline axis; the physical law of soil-pipe interaction due to their relative displacements; and the pipe wall deformation response to axial stress. All three of them are usually well understood but there are still a small number of successful examples of prediction of stresses in such pipelines due to lack of effective algorithms of their accounting for. So here we develop the effective procedure for axial strain and displacement calculation based on notions of basic and correction solutions. The basic solution is algebraically corrected after each iteration step for correction solution, which obtained by numerically efficient transfer matrix method. The role of basic one is very narrow here: first it determines the particular type of law of soil-pipe interaction; second, the resulting solution is considered to be correct when basic and correction solutions coincide. The effectiveness of the algorithm application is shown on number of real examples.

The paper deals with the estimation of the load carrying capacity of the bellow compensator DN100, made of stainless steel AISI 304, which is supposed to be used for providing the necessary level of deformability of main buried gas pipelines in the mining production areas. Experimental investigations of the compensator under cyclic loading by tension-compression with the simultaneous action of working internal pressure are carried out. According to the results of experimental research and numerical simulation, it is shown that such compensators can be used as structural elements of main buried gas pipelines in the mining production areas.Introduction. The problem of the buried pipeline failure as the result of geodynamic processes of the ground surface is very important. According to EGIG [1] 8 % of cases of lossof-piping integrity in the main buried gas pipelines (MBGP) in Europe are caused by their failure as the result of geodynamic processes in the Earth crust. Furthermore, the activity of coal mines also results in the ground surface displacement.The Coal mines influence on MBGP is an important problem on the territory of Ukraine as well since 22.1 km of MBGP [2] have been already located in the areas of their influence and this amount is constantly increasing due to the expansion of mining boundaries.The area of the ground surface where the deformation processes occur as the result of mining production forms so called "shift trough" (see Fig. 1: Нmining depth; mmining capacity; ηmmaximum ground subsidence).As the result of mining development in the shift trough the compression areas and areas of the ground surface tension are formed (see Fig. 1) transmitting their effect on pipeline. Since the axial forces are the main load factor then the horizontal substitution component (vertical is usually neglected) has sufficient effect on the pipeline stressed state.Analyzing the ground displacement kinetics during mining we determined [3] that for the worst case of lava mining (along MBGP) its most loaded areas are subjected to three consequent semicyclestensioncompression and again tension due to the relaxation processes in the ground. Depending on geological conditions, mutual location of the pipe with mining areas the MBGP section can reach the effect area of 15 minings and thus undergo 45 load semicycles.To ensure reliable operation of buried pipelines during lava mining a number of measures aimed at stress state [4 -6] reduction are used, such as:1. Carrying capacity (on the design stage) is increased by: