# Vibration Energy Harvesting from Plates by Means of Piezoelectric Dynamic Vibration Absorbers
## 5 Experimental Results  
### Tests with Impulsive Excitation  
A preliminary experimental modal analysis of the clamped plate was carried out to check the natural frequencies and the modal shapes. Good agreement with analytical results was found. Since the experimental natural frequency of the first mode was slightly lower than the analytical value, the tip mass was increased (\(M_{t}=0.058\) kg); the resulting total mass of the CPDVA was 0.119 kg. For the load case with impulsive excitation, the plate equipped with the CPDVA and the accelerometer was excited through the hammer for modal testing. Even though the hammer hits were exerted by a well-trained operator, there were small errors in the position and orientation of the impulsive force. Hence, to improve the reliability of measurements, the test was repeated seven times. Figure 13 shows the impulsive force applied by the hammer and the measured acceleration and voltage. As shown by experimental data, applying this type of excitation gives good repeatability of the results. The presence of beats in the signal of the voltage generated by the CPDVA highlights the presence of two close natural frequencies in the system. Figure 12: Piezoelectric patch directly bonded to the plate. The measured data were elaborated to retrieve (1) the FRF between the acceleration at the center of the plate and the concentrated load applied to the center of the plate and (2) the FRF between the OC voltage and the concentrated load applied to the center of the plate. The magnitudes of these FRFs are shown in Figure 14 together with the magnitudes of the FRFs predicted by the mathematical model. As expected, the original resonance peak of the plate (15.4 Hz) is eliminated by the CPDVA, and a couple of new peaks are generated: the first at a lower frequency (14.0 Hz) and the second at a higher frequency (16.9 Hz). The presence of the two peaks in the voltage FRF enables energy harvesting in a broad frequency band; this is useful in the case of random excitation. The curves for the different tests are very similar. There is good agreement between the general trend of the experimental FRFs and the FRFs predicted by the mathematical model with concentrated load excitation (Section 2). In particular, the mathematical model predicts the frequencies of the new peaks with an error  
Figure 14: Magnitude of the FRF between the acceleration at the center of the plate and the impulse (**left**) and magnitude of the FRF between the the OC voltage generated by the CPDVA and the impulse (**right**). Experimental and predicted FRFs for the impulse applied to the center of the plate. Figure 13: Experimental results obtained by means of an impulse applied at the center of the plate with CPDVA: impulse (**left**), acceleration at the center of the plate (**center**) and OC voltage generated by the CPDVA (**right**). smaller than 0.5 Hz. The mathematical model slightly overestimates the amplitudes of the peaks of the acceleration FRF when compared with the mean experimental values. Similar behavior is found when the amplitudes of the peaks of the voltage FRF are compared with the mean experimental values, but in this case, the overestimation increases. These differences in the amplitudes can be due to uncertainties in the identification of the damping coefficient of the harvester. In order to evaluate the performance of the CPDVA, the tests with hammer excitation were repeated, substituting the CPDVA with the piezoelectric patch bonded to the plate.