# Influence of Nonstationary Processes in Drill Rigs on the Durability of Structural Elements
An example of a mathematical model for demonstrating the quantitative characteristics of pulsations in a drilling tool was presented. In the article [23], resonant oscillations of an elastic rod subjected to a harmonic load were studied, taking into account the relaxation properties of the material. Features of longitudinal oscillations of a drill string with a compensator during drilling a well on the shelf were considered in the work [24]. In the proposed mathematical model, viscous friction in the pipe material is taken into account, and the significant influence of the compensator on the frequency of oscillations in the string during operation is also noted. In the work [25], the process of transferring the load from the drill string to the bit by exciting the longitudinal and torsional oscillations of the string was studied. Through the application of the finite difference method, a mathematical model was implemented. As a result, it was shown that load transfer by means of vibration processesmakes it possible to avoid the tool becoming stuck and ensures smooth drilling of the well. A mathematical model and computer software for the analysis of dynamic processes occurring in the drilling pipes in the borehole under stuck drill string release by means of an impact mechanism (a jerking device) or a pulse-wave installation, equipped with an electric linear pulse motor, were presented in [26]. The influence of friction forces on the propagation of longitudinal waves in the drill pipe string was investigated. A mathematical model of transverse fluctuations in the pipeline straight section was considered in the article [27]. Such fluctuations occur during the movement of a diagnostic piston in the pipeline. The analysis was based on the method of generalized displacements. The equations of mechanical system motion were derived from the Lagrange scheme equations of the second kind. The article [28] developed recommendations for ensuring the stability of the movement of drill strings, which can be taken into account in practice both at the design stage and during the operation of the drilling equipment. It should also be noted that the drilling equipment can be exposed to cyclic loads (for example, due to the effect of periodic percussion loads, the influence of significant vibration processes, or the peculiarities of the operation of drilling pumps, which are generators of pulsations) [29]. Fatigue damage and microcracks most often occur in places of stress concentration or corrosion localization zones and, under favorable conditions, later grow into macroracks that propagate inward into the material bulk. The character of crack growth depends on a number of operational factors [30; 31; 32], such as the stress intensity factor (SIF) at the macrocrack tip, asymmetry, frequency and shape of the loading cycle, temperature, environment, etc.). Long-term operation of drilling system equipment leads to the accumulation of various types of damage, the initiation of macrocracks, and their subsequent propagation in the material. This negatively affects the durability of individual elements, reduces their efficiency, and increases the risk of unexpected breakdowns. Today, the problems of predicting the operational lifetime of drilling rigs are also relevant and are of crucial importance for their safe and reliable operation, as well as ensuring the structural integrity of the mechanical elements of such structures. In the world literature, various methods of durability assessment and determination of the resource of elements of mechanisms and machines subjected to cyclic loads are presented [33]. Experimental approaches are considered more reliable, but they are expensive and long term. Therefore, researchers usually rely on computer algorithms for predicting the durability of cyclically loaded structural elements. In particular, articles [34; 35; 36] calculated the number of cycles to failure using the AFGROW computing system, which is widely used both in engineering calculations and scientific research.