## 4 Experimental Validation
### Experimental Results  
#### 4.3.1 Normalized Displacement Frequency Responses  
Firstly, broadband excitation are applied onto the free ends of three sandwich specimens. The displacement responses around the clamped ends are obtained and analyzed by the fast Fourier transform (FFT). At this procedure, the frequency resolution set up of the FFT is not high in order to reduce the average time of signal processing. The normalized frequency response curves are illustrated in Figure 8, from which modal data can be obtained.  
As shown in Figure 8, the first six resonant peaks of the short asymmetrical beam are measured, ranging from 1 Hz to 2500 Hz. The first seven resonant peaks of the long asymmetrical beam as well as the long symmetrical beam are obtained, ranging from 1 Hz to 2000 Hz. Since the frequency resolution and average times of the FFT are set relatively low in this procedure, only approximate modal frequencies can be extracted. It can also be observed that more signal burrs arise in the high frequency domain, revealing that vibrations of sandwich beams are harder to be excited and signal noises are more apparent at the higher modes. Hence, the number of FFT average times in high frequency should be given much bigger than those in low frequency in the following analysis.  
Since the theoretical modeling of the VCBTM is based on the assumption of infinite boundary, this approximation is acceptable only at the higher modes [2] and it has been the practice to ignore the first modal results. This practice is also complied with in this study.  
According to the previously obtained approximate modal frequencies, narrow band excitation signals are subsequently applied for each mode. Meanwhile, higher frequency resolutions and bigger number of average times are set up for the FFT. In this way, displacement responses at resonances with more details are guaranteed. Figure 9 reports the normalized frequency response curves under narrow band excitations for three sandwich beams. Figure 9a shows resonant responses of the short  
Figure 8: Normalized frequency responses of sandwich beam specimens: (**a**) short asymmetrical specimen (**b**) long asymmetrical specimen and (**c**) long symmetrical specimen.  
asymmetrical beam at the second to the sixth modes. Figure 9b,c show the second to the seventh mode data for the long asymmetrical beam and long symmetrical beam, respectively.  
It is obvious that frequency response curves in Figure 9 are smoother and clearer than those obtained in the broadband excitation procedure. It can also be observed that the modal frequency response curves are approximately symmetric and nonlinear phenomenon does not arise at resonant peaks. As for the response curve from each mode, an approximate difference of 10 dB is guaranteed between the response at resonance and the value at the lowest or highest frequency. The response curve from the second mode of the long symmetrical beam seems to be an exception, with only 5 dB difference in the narrow frequency band. This is due to the appearance of interference signals at low frequency. Anyway, 5-10 dB response differences are quite enough to extract modal loss factors by the half-power bandwidth method or other damping identification methods. Hence, accurate modal frequencies and other modal characteristics can be extracted from narrow band frequency response curves.