## 4 Evaluation of Prototypes with Edge Damping
### Measurement of the Surface Acceleration and Sound Field Radiation  
Figure 14 shows the results of the surface acceleration and sound field radiation measured according to Sections 4.2 and 4.3 for all three variants. The acceleration level displays the acceleration at different positions on the panel versus frequency. The central axis represents the center position, and the upper and lower values of the y axis represent the positions on the panel. The acceleration data are valid only until 10 kHz. For a more straightforward evaluation, the same frequency range as in the sound radiation measurement is displayed. Below 1 kHz, the radiation is similar for all three variants, caused by the large acoustic wavelength \(\lambda_{A}\) compared to the shorter bending wavelength \(\lambda_{B}\). However, if \(\lambda_{A}\) becomes shorter, then off-axis radiation becomes dominant. Starting at 1 kHz, the off-axis radiation is larger for the Raw Panel than the radiation in the LW, which produces a negative DI. However, if the center acceleration is the largest, especially in the frequency range between 1 kHz and 5 kHz, then off-axis radiation is dominant. Figure 13: (**a**) Measurement setup with a Keyence HK-052 laser at the Technical University of Dresden. (**b**) Overview of the measurement grid: 81 points on the central line are measured. By comparing the surface acceleration, the additional damping layer in the BIF or BOF construction has a smaller impact at lower frequencies (below 1 kHz) and a larger impact at higher frequencies (above 1 kHz). A similar acceleration pattern and standing waves are visible for all variants at low frequencies. With an increase in the wavenumber, the impact of the damping increases. Even if the damping layer is applied to the edges, the impact on the average surface acceleration is large, especially at accelerations close to the boundary. This finding implies that the amount of the standing wave pattern is reduced. The reduced amount of surface acceleration close to the boundary also significantly impacts the directivity response. For both variants BIF and BOF, especially between 1 kHz and 5 kHz, the off-axis radiation is significantly reduced. The effect of coincidence is minimized but cannot be avoided. Damping does not change the bending wavelength, only the ratio of standing waves to traveling waves. Therefore, only the amplitude of the radiated wave can be reduced. This effect can be clearly seen by comparing the results of Panel-Raw to those of Panel-BIF or Panel-BOF. Furthermore, the prototype BIF shows a slight shift of \(f_{c}\) compared to those of RAW and BOF. The increased coincidence frequency results from the additional mass of the damping layer, even when it is placed close to the frame. The impact of the additional damping layer below 1 kHz is negligible, and the same directivity response occurs. The upper-frequency limit of 15 kHz is caused by the break-up mode of the exciter voice-coil former, which is similar for all variants. Figure 15 shows the calculated DI for all variants. The results are confirmed, and the prototypes with additional damping have a better DI than the raw panel below \(f_{c}\). Above \(f_{c}\), the damping has less influence. Figure 14: Comparison of the surface acceleration and directivity response of all three variants: Panel-Raw, Panel-BIF and Panel-BOF. Both variants with additional damping layer generate an improved directivity response, which can be expressed by the mean value and the standard deviation. The results of the mean value and standard deviation are presented in Table 2. It becomes visible that the edge damping has the largest influence in the frequency range below the coincidence frequency (1 kHz-7.5 kHz). The mean value of the DI is increased from \(-\)3.94 dB to \(-\)1.40 dB by 2.54 dB for the variant BIF and to \(-\)1.49 dB by 2.45 dB for the variant BOF. Furthermore, the standard deviation is also reduced from 3.03 dB to 1.92 dB by 1.14 dB (BIF) and to 2.92 dB by 0.11 dB (BOF).