## 1 Introduction
This behavior can cause coloration and unusual spatial artifacts [8] and needs to be improved. The frequency with the lowest DI is the coincidence frequency \(f_{c}\), where the acoustic wavelength equals the bending wavelength in the structure. Figure 1: Polar angle-dependent radiation of a studio monitor in comparison to a flat panel loudspeaker prototype measured in 2 m distance with a 2\({}^{\circ}\) angular resolution. Both measurements were referenced to the same averaged SPL value of 80 dB in the frequency range from 100 Hz to 1000 Hz. Figure 2: Directivity index calculated as the difference in the LW (\(\pm 30^{\circ}\)) and the front hemisphere (FH, \(\pm 90^{\circ}\)) for the studio monitor and flat panel loudspeaker. Several approaches have already been used to investigate the problem of inhomogeneous radiation. Differentiation between the frequency ranges below coincidence and above coincidence is important. Both frequency ranges tend to have a negative DI, but improving the DI requires significantly different constructive changes. Above \(f_{c}\), the acoustic wavelength \(\lambda_{A}\) is shorter than the bending wavelength \(\lambda_{B}\), and the sound can only be radiated in a frequency-dependent spatial direction. This behavior can be solved by decreasing \(\lambda_{B}\) and increasing \(f_{c}\) by using different panel properties [10] or by using a complex panel layup, e.g., a sandwich structure [11]. These changes are not considered in this paper. Below \(f_{c}\), the sound radiation can be predominantly described by near-field effects [12]. The radiation is dominated by the mode shape and amplitude distribution and can be optimized by changing the vibration pattern of the panel. [PERSON] [13] combined a genetic algorithm with a numerical simulation model to calculate the ideal exciter position in terms of the best possible efficiency and directivity. An optimized exciter position improves the directivity result, but strong radiation to the sides remains. [PERSON] [14] investigated the possibility of generating a directional sound field by using an exciter array on a clamped panel. The authors were able to experimentally demonstrate that an appropriate directivity can be achieved by using multiple exciters. This option results in a higher cost and higher complexity due to the multiple exciters, amplifiers and digital signal processor (DSP) outputs. A simpler method was investigated in an earlier study, which considered the influence of boundary conditions on the DI [9]. A more homogeneous characteristic of the DI was achieved by decoupling the edge with rubber and bitumen. The aim of the present paper was to improve the directivity response below the coincidence of an existing panel by changing the resulting vibration pattern using edge damping. This approach changes the proportion of traveling waves relative to standing waves, which causes amplitude redistribution. Both effects influence the sound radiation and the directional characteristics of the flat panel loudspeaker. In Section 2, the directivity of a flat panel loudspeaker prototype is analyzed in detail by comparing the frequency-dependent surface acceleration with the radiated sound pressure. In the third section, numerical investigations are conducted to understand the root causes of the off-axis radiation and the influence of damping. With numerical simulation methods, the DIs of individual modes are calculated, and the root cause of the negative DI is visualized. Furthermore, the simulation model is used to differentiate between standing waves and traveling waves to analyze the impact of damping on the directivity characteristics. In the last section, different prototypes with edge damping are built, and measurements of directivity and surface acceleration are performed with real prototypes. This experiment demonstrates that additional damping significantly improves the directivity in the region below the coincidence frequency without losing sensitivity in the LW.