Modal analysis of a hydrogen-damaged pipe as shell inhomogeneous on thickness

Hydrogen corrosion of main gas and oil pipelines often leads to accidents. It is necessary to assess the life of hydrogen-weakened pipes. An inner layer with deteriorated mechanical characteristics is formed in them under pressure of hydrogen-containing medium. In the paper the calculation of free vibrations of such a tube taking into account the degradation of its material is performed. The tube is modeled as a bilayer cylindrical shell according to the classical theory. Influence of hydrogen-impacted layer is taken into account when calculating stiffnesses and displacement of neutral line of the shell. Three variants of averaging of parameters determining the stiffness of the shell are considered, numerical experiments are carried out and the natural frequencies of the shell are found. Comparison with calculations using the method of finite elements in the ANSYS software made it possible to estimate the degree of applicability of each version of averaging. The method of averaging Young's modulus over the thickness of the shell does not "feel" asymmetry of layers relative to the neutral line. The method of adding a correction for the neutral line radius of the shell works satisfactorily for axisymmetric and beam modes. The next more accurate approximation is to average the shell stiffnesses over its thickness with the reduced radius. This method allows us to obtain satisfactory results in a wide enough frequency range and for the modes related to the deformation of the shell cross section. A method for the principle reconstruction of the parameters characterizing the stiffness of the shell using three experimentally obtained fixed frequencies has been proposed. On the basis of these studies formulas are proposed which allow to reconstruct parameters of weakening of pipe material, as a result of hydrogen corrosion, both in thickness and in time from the frequency characteristics of the pipe.