## 2 Materials and Methods
### Dynamic Response Measurement Systems for AIEs with Translatory Motion  
AIEs are intended for use over wide ranges of frequencies, forces and displacements, and therefore should be investigated over these ranges. To cover this wide range, a hydraulic shaker (for large displacements and forces) and an electrodynamic shaker (for high frequencies) are chosen. The use of electrodynamic shakers is common for the investigation of vibration behavior [27,33]. Electrodynamic shakers are found in a variety of sizes, frequency ranges and forces. The working principle introduces certain restrictions in the low frequency domain. The introduction of static payloads decreases the maximum acceleration when no static compensation is present. This is caused by static deflection and the limited stroke range [34]. Static compensation can either be introduced by external pneumatic systems or by application of DC current to the shaker input. The tuning of external compensation  
Figure 2: (**a**) Hydraulic test bench for low frequencies adapted from [32]; (**b**) electrodynamic test bench for high frequencies. systems can however be challenging and the application of DC current heats up the system, inevitably reducing the dynamic capabilities [34]. The use of hydraulic shakers are generally beneficial for environments that require relatively large force over a wide range of distance, while the velocity is limited. The test range depends on a number of factors such as pump and servo valve flow rate capacity. The frequency range generally reaches up to 40 Hz [27]. In this paper, a hydraulic test rig represents the low frequency test bench. To evaluate the mechanical properties of the test object the one-dimensional servo hydraulic test rig shown by [PERSON] et al. [8] is used. Dynamic vibration tests with forces up to 125 kN and velocities up to 0.6 m/s are possible. An acceleration of 10 m/s\({}^{2}\) leads to a frequency range from 3 to 23 Hz, since lower frequencies at this acceleration would result in too high displacements. Figure 3a shows the test setup for testing of the compliant element A at the low frequency test bench (FGB-630, Fertigungsgeratebau Adolf Steinbach GmbH and Co. KG, Salz, Germany). The used force sensor (59M/10 kN, Hottinger Briel and Kjaer (HBM) GmbH, Darmstadt, Germany) and acceleration sensor (3D 50g 356A15, PCB Piezotronics Inc., Depew NY, USA) are newly calibrated by the manufacturer. The force sensor weighs 0.9933 kg, the acceleration sensor with its base weighs 0.0144 kg and the adapter between the force sensor and tested element weighs 0.3533 kg. Half the mass of the force sensor plus the mass of the acceleration sensor (Section 2.5) results in the moved mass of the low frequency test bench \(m_{sensor,~{}lowfreq}=0.863\) kg (Table 1). To transduce and record the signal the HBM QuantumX System (MX1601 and MX840B, Hottinger Briel and Kjaer (HBM) GmbH, Darmstadt, Germany) is used at a sample rate of 600 Hz for the investigation of frequencies up to 23 Hz. Figure 3b shows the high frequency test bench (M124M, ETS Solutions Europe, Loffenau, Germany). Kistler (9027C, Kistler Instrumente AG, Winterthur, Switzerland) and the accelerometer (3D 50g 356A15, PCB Piezotronics Inc., Depew, NY, USA) are calibrated. The moved mass is determined via a vibration test, since in the assembled state the moving mass cannot be determined directly. Furthermore, the moving mass of the assembled subsystem may differ from results obtained by conventional weighing. This may be due to a force bypassing in the bolted connections or due to unknown inertia forces for example by cable attachments at the sensors. A vibration test at frequencies from 10-500 Hz at a 5 Hz interval resulted in a force measured by the force transducers equivalent to a mass of \(m_{sensor,~{}highfreq}=1.133\) kg (Table 1). This force poses a baseline for the dynamic calibration of the flange and further dynamic measurements.