**5. Conclusions**

In the present article, the vibration characteristics of a radial turbine bladed disc of a marine engine turbocharger were investigated. Starting with the analysis of structural dynamic properties of cyclic symmetry components, basic procedures were transferred to special problems of bladed discs of marine turbocharger radial turbines and expanded. In particular, the assignment of individual peaks in the measured transmission functions to the corresponding mode shapes was performed using a carefully designed FE model, without the need to apply an expensive scanning vibrometer. In addition, the distribution of the strain energy between the disc and the blade calculated by the FE model is a next parameter that allows the systematic assessment each of the large number of modal shapes present in this complicated structure. The mode shapes with predominant strain energy in the blade are thus referred to as blade-dominated. Depending on the criterion of distribution of the strain energy among the blades and the disc, some modes can be called mixed. The transfer functions shown above also record these mixed modes such as matching peaks, but their e ffect on blade stress is not significant. Disc dominant modes do not occur in the examined frequency range of the analysed marine engine turbocharger radial turbine. The reason for this is the massive disc and the rigid connection of the blades to them.

Based on the results of the measurements described above, it was possible to create a 3D mistuned FE model of the turbine bladed disc. Creation of this model is based on individual adaptation of the modulus of elasticity to individual blades using optimization algorithms. The vibration behaviour of the real bladed discs can be achieved with su fficient accuracy by such 3D models, unlike methods that are based on the use of substructures and do not describe the frequency splitting due to mistuning with the necessary accuracy. Since the description of the optimization algorithm and the creation of the 3D model of the mistuned turbine wheel would go far beyond the possible size of this article, this topic will be the subject of a separate publication.

With regard to industrial application, it should be noted that an improvement in manufacturing accuracy is only conditionally recommended, since increasing the manufacturing accuracy of the blades would entail unacceptable financial costs. Rather, it is important to determine the inclination of individual vibration modes in order to tend large increases in stress. It should be noted that large stress increases are always accompanied by strongly localised modes. However, strongly localised mode shapes can only occur if the tuned bladed disc system has a su fficient number of node diameter vibrations in a relative frequency proximity. These cases can be identified already in the early stages of development if a suitable FE blade disc model is used. Together with the described e ffective mistuning identification method of integrated bladed discs, the development of new marine engine turbochargers can be significantly accelerated. Another added value of the method is the possibility of its relatively easy automation, both in terms of measurement and its subsequent processing and evaluation. The turbocharger manufacturer can thus obtain complete statistical information on the parameters of the blade discs in relation to the mistuning caused by various influences in the production process.

**Author Contributions:** Conceptualization, V.P.; methodology, V.P. and P.K.; software, P.K. and O.F.; validation, P.K. and A.L.; writing—review and editing, V.P. and P.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors gratefully acknowledge funding from the Specific research on BUT FSI-S-20-6267.

**Acknowledgments:** The authors thank the Brno University of Technology for support. **Conflicts of Interest:** The authors declare no conflict of interest.
