## 5 Summary  
This paper focuses on optimizing the directivity of flat panel loudspeakers below the coincidence frequency by minimizing the off-axis radiation. This problem can be solved with additional damping on the panel, which changes the proportion of traveling waves relative to standing waves. Furthermore, this approach leads to amplitude redistribution on the panel. Above the coincidence frequency, only the panel properties are dominant, which cannot be affected without changes in mass or stiffness. This robust and straightforward method is comprehensively described in the sections of this paper. In Section 2, the directivity responses of individual modes are analyzed and provide knowledge about the negative DI. The directivity is the result of the ratio of the bending wavelength to the acoustic wavelength. Therefore, differentiating between the frequency ranges below and above coincidence is important. Above coincidence, the acoustic wavelength is shorter than the bending wavelength, and the sound wave couples almost perfectly to the air with maximum radiation efficiency. However, the energy can be radiated in only one frequency-dependent spatial direction. The behavior can be improved by using different panel properties or a complex panel layup. Below the coincidence frequency, the sound radiation can be predominantly described by near-field effects, and the radiation is dominated by the mode shape and amplitude distribution on the panel. Especially symmetrical mode shapes tend to a perfect acoustic cancellation in the panel center and sources at the edges remain. Due to the distance between the remaining sources, complex directivity responses are generated. A redistribution of the deflections can be achieved by constructive modifications or by damping. Increasing the damping changes the wave pattern from standing waves towards traveling waves. In the following section, a numerical simulation model is set up to analyze the frequency-dependent radiation mechanism of three different damped HPL-panels. The numerical simulation models have shown that an increased damping value reduces the sources at the edge of the panel compared to the center of the panel. The decreased amount of standing waves will generate less off-axis radiation, and the panel motion is concentrated in the region of the force application point. In the last section, real prototypes with two different types of edge damping are introduced and compared with the initial state without damping. For this purpose, the results were determined by measuring the panel motion using laser vibrometry and the directivity in an anechoic chamber. In principle, the existence of specific eigenmodes can be demonstrated by the panel motion at low frequencies. With increasing frequency, the modal pattern has a higher complexity, and the deflection is concentrated at the center of the panel. Between 1 kHz and 6.2 kHz, the dominant radiation off-axis is particularly noticeable, which yields a negative DI. The additional damping optimizes the DI, especially in the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Averaged SPL** & & **Variants** & \\
**1 kHz-10 kHz** & **Panel-Raw** & **Panel-BIF** & **Panel-BOF** \\ \hline LW (\(\pm 30^{\circ}\)) & 71.68 dB & 70.98 dB & 70.91 dB \\ Difference to Panel-Raw & & \(-0.70\) dB & \(-0.77\) dB \\ FH (\(\pm 90^{\circ}\)) & 76.20 dB & 72.98 dB & 73.46 dB \\ Difference to Panel-Raw & & \(-3.22\) dB & \(-2.74\) dB \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Averaged SPL in the LW compared to the FH in the frequency range of 1 kHz to 10 kHz. angular range, which would yield a lower listening preference rating. The impact on the LW radiation is low. The directivity response of the damped panel is more homogeneous, measured by a higher mean value and lower standard deviation. The best result can be achieved with damping attached to the panel on the inside of the frame. This finding underlines the result that the additional damping applies more to the FH and has a lower impact on the LW response.