On the relationship of natural oscillation frequencies and critical loads in assessing the rigidity of load-bearing elements of carriage structures
The regulatory and technical documentation clearly defines the requirements for assessing the bearing capacity of rolling stock units, for example, to check the design being developed for loss of stability under the influence of compressive loads. This involves performing verification by calculation methods. The article considers the possibility of determining the critical level of external overpressure on the shell of the tank cauldron on the basis of experimental data on the minimum frequency and shape of natural oscillations. In order to solve this problem, the differential equation of flat cylindrical shells is used. The equation used was proposed by Donnell and has proven itself well in calculation of cylindrical shells, in particular cauldrons of tank cars. The peculiarity of the proposed solution lies in a certain analogy of the mathematical description of the processes of loss of stability and natural oscillations. As a result of transformations of the differential equations under consideration, an expression is obtained that connects the critical level of external overpressure and the natural oscillation frequencies of the objects under consideration. Numerical values of the studied parameters are given, the reliability of which is confirmed by similarity with the data given in previously published sources. Recommendations are given on application of the proposed approach in engineering verification of carriage structure elements stability. The necessity of taking into account the forms of oscillations and loss of stability when determining the level of critical pressure by the obtained expression is shown.