# Vibration Reduction on Circular Disks with Vibroacoustic Metamaterials
## 4 Conclusions  
In the presented work, the behavior of a VAMM for out-of-plane vibration reduction of a thin-walled circular disk has been investigated experimentally in the rotating state with a stationary observer up to 3000 rpm. The leading research questions are whether the stop band still exists under rotation, whether it is subject to a frequency shift or whether it is narrowed down by split modes traveling into the stop band with increasing rotational speed. The study was performed experimentally because a numerical study is bound to limitations since a VAMM is always a non-axisymmetric system. In order to be able to experimentally investigate a rotating disk with an embedded VAMM, such a disk firstly was developed based on numerical simulations in the non-rotating state. The dimensions of the disk were adopted from a circular saw blade usually used in woodworking. The stop band was tuned to a frequency range of approx. 2000 Hz to 3000 Hz where circular saw blades are often loudest. For the experimental investigation, a measurement setup consisting of a stationary LDV for measuring the out-of-plane vibrations and an automatic impulse hammer for excitation is suggested. With this setup, Campbell plots were recorded for two different measurement points--one within the resonator array of the VAMM and one on the circumference of the disk. For the measurement point at the circumference, no stop band was obtained since no resonators were placed at the circumference. The inner measurement point indicates a stop band in between approx. 2000 Hz and 3000 Hz that does not shift in frequency with increasing rotational speed. Adjoining modes that split up propagate into the stop band region, narrowing it down symmetrically by approx. 200 Hz. As a result, it can be stated that the gyroscopic and centrifugal forces do not have a significant influence on the formation of the stop band. Furthermore, the results show that a VAMM for a thin-walled disk can be numerically designed in the non-rotating state with good accuracy. Adjoining modes that are on the verge of propagating into the stop band can be accounted for with analytical estimations as shown in the last section of this work. For that, the number of nodal diameters needs to be obtained from numerically evaluated mode shapes.  
This work contributes to the field of VAMMs for vibration reduction on thin-walled rotors both in terms of the methodology used for the development and in terms of the experimental validation of such a system. The results are applicable to other technical systems where out-of-plane vibrations of thin-walled rotors such as gears, brake disks, saw blades, fans, etc., are to be reduced.  
Conceptualization, S.R.; methodology, S.R. and R.S.; software, S.R. and R.S.; validation, S.R. and R.S.; formal analysis, S.R. and R.S.; investigation, S.R. and R.S.; resources, S.R. and R.S.; data curation, S.R. and R.S.; writing--original draft preparation, S.R. and R.S.; writing--review and editing, S.R., R.S., W.K., H.A. and S.H.; visualization, S.R. and R.S.; supervision, S.H., W.K. and H.A.; project administration, S.R.; funding acquisition, S.R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
LDV laser Doppler vibrometer  
MP measurement point  
VAMM vibroacoustic metamaterial