The effects produced by the rain on the roof excitation are now analysed considering plots (e) and (f) of Figure 11. Considering first plot (e), it is noted that also in this case the spectrum of the kinetic energy is characterised by well separated resonances, which tend to become wide band crests as the frequency, and thus modal overlap effect, grows. However, contrasting this graph with the two kinetic energy graphs (a) and (c), it is clear that, when the panel is excited by a uniform distribution of uncorrelated forces, all resonant modes are efficiently actuated. This is due to the fact that, in contrast to acoustic excitations, the rain on the roof excitation is composed by a uniform distribution of fully uncorrelated forces, which equally couples with all natural modes of the panel. Hence the amplitude of the resonance peaks in the spectrum for the kinetic energy tends to be uniform, since the coupling between the ROR excitation field and modal response of the panel does not vary from one mode to another. The relative amplitude of the resonance peaks are solely dictated by the damping effect and by the overlap with neighbouring modes. As a result, at frequencies above the fundamental resonance of the panel, the amplitudes of the resonance peaks are rather uniform and the mean spectrum falls with a 3 dB/octave rate instead of the 6 dB/octave rate found for the plane wave and diffuse acoustic excitations. Thus, as one would expect, the mean spectrum of the panel kinetic energy due to a rain on the roof excitation follows that of the squared point mobility function for the ratio between the transverse velocity and transverse force. This trend carries on also around and beyond the critical frequency at about 7.54 kHz. This is due to the fact that there are no favoured frequencies, such as the acoustic coincidence frequency, where the excitation field effectively couples with the structural response of the panel.
Moving on to the radiated sound power, comparing plot (f) with plots (b) and (d), it is noted that the spectrum of the radiated sound power generated by a rain on the roof excitation presents remarkable differences with respect to the spectra generated by an acoustic plane wave or diffuse field excitations. For instance, in contrast to what found with the acoustic excitations, at low frequencies the sound radiation is characterised by many more resonance peaks, which are due to efficiently and non efficiently radiating modes. Thus the radiated sound power is characterised by a comparatively denser distribution of resonance peaks, which, at low frequency, are well separated and then, as the frequency and modal overlap rise, become wide frequency band crests characterised by the overlap of multiple resonant modes. Moreover the level of the spectrum of the radiated sound power remains constant up to about the critical frequency where it shows the typical wide band ridge. All this is due to two concomitant effects. Firstly, as discussed above, the rain on the roof uniform distribution of uncorrelated point forces equally excites all natural modes of the panel. Secondly, as discussed in (Fahy and Gardonio 2007), in contrast with the modal sound radiation, the sound radiation produced by point forces is constant with frequencies, thus it is very effective also at frequencies well below the critical frequency. Moving back to plot (f), at higher frequencies around the critical frequency at about 7.54 kHz, the sound radiation shows the typical wide frequency band ridge with multiple resonance peaks, which is due to the fact that all structural modes effectively radiates sound.