## 3 Results and Discussion
### Evaluation of the Dynamic Response of the Compliant Elements  
The evaluation of the possibilities of the adapted approach (Sections 2.2 and 2.3) is shown in this section for the compliant elements A and B (Figure 4). The measured force, analytically given by Equation (1) results from the stiffness, damping, and mass properties of the element. The resulting force is dependent on displacement, velocity and acceleration, which are derivatives of each other. Since AM, MI and AS are given by force over acceleration, velocity and displacement (see Equation (3)), they are inverse derivatives as well (see Equation (5)). Figure 9 shows the test results of the compliant element A (Figure 4) in form of AM, MI and AS, as well as the phase of AS. All plots have their advantage in analyzing specific parts of the test objects behavior. The measured data points for \(AM_{meas}\), \(MI_{meas}\) and \(AS_{meas}\), are marked as dots and the calibrated ones \(AM_{testobj}\), \(AM_{testobj}\) and \(AS_{testobj}\) are marked as asterisks. From the nearly constant part of \(abs(AS)\) in Figure 9 in front of the first natural frequency results that the behavior of compliant element A is dominated by its stiffness. A phase angle of AS near zero or \(n\cdot\pi\) also shows a stiffness-dominated behavior. The natural frequency can be determined at the phase change and the point of least necessary force to excite the element, which therefore is also described by the low point of AM, MI and AS. With increasing frequency, the acceleration increases (Equation (2)), and with it the force component of mass multiplied by acceleration. For AS and MI in Figure 9 this can be seen as an increase over frequency, especially above the natural frequency. At high frequencies the force component of the mass dominates this behavior; therefore, in the plots of AM,  
Figure 9: FRFs AM, MI, AS and its phase directly measured and the calibrated FRFs of the compliant element A over frequency. they converge to an asymptote, which corresponds to the real vibrating mass. From the plot MI, the damping behavior can be derived, since at the natural frequency (\(\omega_{0}=\sqrt{k/m}\)) the resulting force from mass and stiffness cancel each other and only the damping force remains (Equation (1)). When determining the stiffness in the lower frequency range, the influence of calibration by mass cancellation is negligible. In addition, the influence of the \(HI_{pp}\) function is less than 2% for the low frequency test bench (Section 3.2). The value of the deepest point of MI is located at the natural frequency and is smaller for the calibrated measurement. The resulting force from the non-calibrated, as well as from the calibrated measurement, dissolve in both cases with the force resulting from stiffness. The remaining damping force is at a higher frequency, respectively higher velocity, which is why MI is lower. In all frequency ranges, except very low frequencies and at the natural frequency, the mass cancellation introduced by [PERSON] [26] and the _measurement systems_\(FRF\)\(HI_{pp}\) by [PERSON] [27] have a clear influence on the results. Noticeable in all diagrams is the deviation of the natural frequency between the non-calibrated measurement at approximately 80 Hz and the calibrated measurement at approximately 190 Hz. In the calibrated measurement, the mass \(m_{sensor,\ highfreq}=1.133\) kg is subtracted, which directly affects the natural frequency. In addition, the asymptote, approached by AM at high frequencies, differs between the non-calibrated and calibrated measurement by the mass \(m_{sensor}\). The phase angle of AM, MI and AS is also crucial for vibration analysis. A phase angle of \(arg(AS)=0\) shows that force and displacement are in phase and thus describe an ideal spring. A phase angle of \(arg(MI)=0\) is equivalent to \(arg(AS)=\pi/2\) and describes that force and velocity are in phase and therefore an ideal viscous damper. A phase angle of \(arg(AM)=0\) is equivalent to \(arg(AS)=\pi\) and describes an ideal mass.