The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for evaluating the results of a natural transverse vibration analysis as generated by finite element (FE) models of a shaft with compound geometry. The effectiveness of the suggested approach is tested using an arbitrarily chosen model of the injection pump shaft. The required analytical models of the transverse vibrations of stepped shafts are derived based on the Timoshenko thick beam theory. The separation of variables method is used to find the needed solutions to the free vibrations. The eigenvalue problem is formulated and solved by using the FE representation for the shaft and for each shaft-simplified model. The results for these models are discussed and compared. Additionally, the usefulness of the Myklestad–Prohl (MP) method in the field of preliminary analysis of transverse vibration of complex shaft systems is indicated. It is important to note that the solutions proposed in this paper could be useful for engineers dealing with the dynamics of various types of machine shafts with low values of operating speeds.

In this paper the experimental studies of the screen working in the parametric resonance condition are discussed. The investigations are conducted for laboratory parametric resonance screen. The measuring test is performed for four cases of tension force values. The full sheet metal instead of the sieve is used. For each considered case the natural frequency of the plate and the parameter modulation frequency are determined. The achieved results are presented and discussed. It is shown that the highest sieve plate amplitude is obtained when the parameter modulation frequency is two times larger than natural frequency of the sieve plate. This parametric resonance vibration was observed only for tension force equal to 4000 N because of the rotational speed limits of electrical vibratos.

The paper discusses the issue of transverse natural vibrations of toothed wheels intended for operation in aviation power transmission systems or in the transmission of aircraft engine aggregates. The discussion was conducted using wheels with straight, oblique and circular-arc teeth, as well as with a full wheel disc and a wheel disc with eccentric holes. In the analysis process, simplified toothed ring models were proposed for each gear in the form of rings made of a hypothetical material with satisfactory physical properties (equivalent values of Young’s modulus and the density). In the proposed models were also taken into account the properties of cyclic symmetry exhibited by the studied objects. The calculation process was carried out using the finite element method and the commercial ANSYS software. The influence of the type and size of finite element on the quality of the obtained results was also investigated. The main part of the work concerns the assessment of the usefulness of the proposed simplified models of the analyzed wheels in the vibration simulation process. In order to confirm the correctness of the simulation research methodology, for one of the analyzed wheel cases, the numerical simulation results were verified experimentally on a real object. The article concludes with remarks and conclusions regarding the obtained results. The issues presented in this paper may be useful in engineering practice related to vibrations of circularly symmetric systems (in particular, gear wheels).