The work is focused on the problem of vibrating beams with a variable cross-section fixed on a rotational rigid disk. The beam is loaded by a transversal time varying force orthogonal to an axis of the beam and simultaneously parallel to the disk's plane. There are many ways of usage of the technical moveable systems composed of elements with the variable cross-sections. The main applications are used in numerous types of turbines and pumps. The paper is a kind of introduction to the dynamic analysis of above mentioned beam systems. The equations of motion of rotational beams fixed on the rigid disks were derived. After introducing the Coriolis forces and the centrifugal forces, the transportation effect in the mathematical model was considered. This particular project is the first stage research, where there were proposed certain solutions of problems connected with the linear variable cross-sections systems. The further investigation considering the nonlinear systems has been proceeding. The results, analysis and comparison will be presented in the future works.

The study of symmetrical and non-symmetrical effects in physics, mathematics, mechanics, medicine, and numerical methods is a current topic due to the complexity of the experiments, calculations, and virtual simulations. However, there is a limited number of research publications in computational biomechanics focusing on the symmetry of numerical head models. The majority of the models in the researched literature are symmetrical. Thus, we stated a hypothesis wherever the symmetrical models might be more applicable in numerical analysis. We carried out in-depth studies about head symmetry through clinical data, medical images, materials models, and computer analysis. We concluded that the mapping of the entire geometry of the skull and brain is essential due to the significant differences that affect the results of numerical analyses and the possibility of misinterpretation of the tissue deformation under mechanical load results.

The scientific aim of this paper is to analyse the topicality of the turbocharger explosions and to attempt to answer the question of whether some technical characteristics of the engine can be perceived as directly connected with the risk of the turbocharger explosion. Moreover, our objective was also to calculate the turbocharger explosion probability. This article presents the results of a quantitative and qualitative analysis of 42 explosions of marine main engine turbochargers occurring between 1977 and 2022. The number of explosions was analysed, and the average and instantaneous frequencies of turbocharger explosions each year were determined. An analysis was performed of the number of explosions with respect to the age and type of ship on which the accident occurred. An analysis of the contribution of different types of main engine to the studied population of explosions was also carried out. Criteria such as the number of strokes, engine speed, type of crank-piston mechanism, cylinder arrangement, engine power per cylinder, and number of cylinders were considered. An analysis was carried out of the disasters that had occurred, considering the contribution of the various engine manufacturers. An integrated distribution of the number of turbocharger explosions by year was presented, considering the engine speed, the maximum continuous rating of the engine, and the engine design. The analysis did not indicate a significant correlation between the type of ship and the number of explosions that occurred. More than half of the analysed population of explosions (median) occurred on vessels no older than 15 years. It is highly likely that engine type does not directly affect the number of turbocharger explosions and the risk of explosions. On the other hand, it is not possible to exclude the influence of the individual characteristics of an engine built to a particular manufacturer’s design on the magnitude of the risk of a turbocharger exploding during engine operation. Considering the number of ships worldwide, the probability of an explosion in a given year on a given ship is not less than 1.61 × 10⁻⁷.