## 5 Conclusions  
The article presented deals with the issue of the vibration of turbocharger impellers, in particular, with effective methods for determining their mistuning. The described acoustic method does not require the application of an expensive laser scanning techniques or a single-beam laser, but assigns the appropriate mode shapes to the individual detected peaks of the FFT analysis of the blade response using a computational finite element model. Simultaneously with the acoustic measurement, a laser vibration measurement at the blade tips was performed and the respective frequency analyses were evaluated. From a comparison of the FFT analysis determined by the acoustic method and the use of the laser vibrometer, it is obvious that both procedures lead to identical results.  
A significant advantage of the presented acoustic method over laser Doppler vibrometry is its relative simplicity and considerably lower costs for measuring instruments. The computational model makes it easy to decide, among other things, what type of mode shape it is. In addition to showing the deformations of the impeller structure or animating the shape oscillation for individual modes, another important criterion is available. According to the distribution of specific strain energy in the sector of one blade calculated by finite element model, it is possible to decide whether it is a blade dominated, disc dominated or a mixed mode shape. Mode shapes in which the specific strain energy contained in the blades exceeds 90% can be considered blade dominated. Mode shapes in which the proportion of the specific strain energy in the blades is between 90 and 65% can be considered mixed. Mixed modes also occur in the impeller according to Figure 1, as shown by the results of the computational models and the results of the measurements, but they do not have a large effect on the stress in the blades. Disc-dominated modes were not detected in the investigated impeller which obviously follows from the robust design of the disc and the rigid connection of the blades to it. In the frequency spectrum evaluated from acoustic measurements, some peaks belonging to mixed  
Figure 13: Eigenfrequency mistuning of turbine impeller blades of Modes 1–7.  
modes are highlighted compared to laser measurements. This can also be considered as a certain advantage over laser measurement in the case of bladed discs, in which resonant states corresponding to mixed or disc dominated modes would occur in the operating speed range. Similar measurements were performed for other cases of turbine wheels of various sizes, from turbochargers of diesel engines of heavy commercial vehicles to petrol engines of passenger cars. In all cases, the results of acoustic and laser measurements were found to be identical.  
The presented acoustic method can therefore be considered as a full-fledged alternative to laser vibrometry, while the cost of the necessary measuring equipment is much lower. Its application compared to laser Doppler vibrometer measurement could be limited only in the case of very small impellers whose blade eigenfrequencies would exceed the measuring frequency range of the microphone used.  
Conceptualization, V.P.; methodology, V.P. and P.K.; software, P.K. and O.F.; validation, P.K., A.L. and A.P.; writing--review and editing, V.P. and P.K.; All authors have read and agreed to the published version of the manuscript.  
The authors gratefully acknowledge funding from the Specific research on BUT FSI-S-20-6267.  
The authors thank to Brno University of Technology for support.  
The authors declare no conflict of interest.