# Vibration Reduction on Circular Disks with Vibroacoustic Metamaterials  
[PERSON]  
1 Fraunhofer Institute for Structural Durability and System Reliability LBE, 64298 Darmstadt, Germany; [EMAIL_ADDRESS] (R.S.); [EMAIL_ADDRESS] (W.K.); [EMAIL_ADDRESS] (H.A.); [EMAIL_ADDRESS] (S.H.)  
1 Fraunhofer Institute for Structural Durability and System Reliability LBE, 64298 Darmstadt, Germany; [EMAIL_ADDRESS] (R.S.); [EMAIL_ADDRESS] (W.K.); weiam.keald@bf.fraunhofer.  
certain frequency range [5] for the overall structure. Within this frequency range, a stop band for elastic waves occurs, where no free wave propagation is possible. A schematic VAMM with an exemplary stop band can be seen in Figure 1.  
While there are a large variety of works that have focused on the application of VAMMs on non-rotating structures, for example, in aviation and space [6; 7], the automotive industry [8] and machinery [9; 10], there is limited information regarding their behavior in the rotating state, though thin-walled rotors often face severe vibration problems. For example, the sound emitted by a circular saw blade predominately goes back to the vibrations of the saw blade [11] which are excited by the sawing process. Thin-walled lightweight gears, rotating at large rotational speeds, become excited by the engagement of the teeth. This can lead to extensive gear noise being emitted by the gear body or the housing which is excited by vibrations traveling over the shafts. In addition, there are multiple other examples of rotating structures facing vibration issues, like brake disks, fans in turbo machines and compressors. In rotating structures, centrifugal and gyroscopic forces act on the resonators of the VAMM, and when observed from a stationary observer, modes split into a forward and backward propagating wave. These special effects have to be investigated for a VAMM in the rotating state.  
While VAMMs have been investigated for the reduction of torsional waves [13; 14; 15] and bending waves [16; 17; 18; 19] of spinning shafts, there is just a limited amount of works focusing on the reduction of elastic waves in thin-walled rotors. [PERSON] et al. [20] numerically investigated a so-called metastructure on a thin-walled gear, where the spring element of the resonators is machined out of the gear. However, the investigation was not carried out in the rotating state. [PERSON] et al. suggested investigating the effects of gyroscopic forces that act on the resonators. In an experimental work by [PERSON] et al. [12], the authors studied the behavior of a VAMM integrated into a circular saw blade. The spinning saw blade was excited by an impulse hammer and the resulting vibrations were measured with a stationary laser Doppler vibrometer (LDV). The stop band characteristic was validated for a rotational speed of up to 1000 rpm. The work was limited by the signal-to-noise-ratio of the measurement setup. Though the stop band was identified in the rotating state, it was not possible to examine whether the stop band is narrowed down by adjacent modes traveling into the stop band or whether the stop band travels with increasing rotational speed due to a shift in the resonator's eigenfrequency as a result of centrifugal forces. The presented study has the aim of answering these questions with an experimental investigation. Methodically, it follows the work of [PERSON] et al. [12] with the improvement of the test setup and the investigation of a circular disk, which is a more general structure than a saw blade. An experimental study is chosen since the numerical simulation of non-axisymmetric systems is subject to limitations [21].  
Figure 1: **(a)** Schematic of a VAMM, (**b**) schematically depicted stop band in the frequency domain. Source: compare [12].