## 4 Experimental Results: Short Beams
### HNSW-Transducer Measurements
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cast Day**} & \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Top**} & \multicolumn{2}{c}{**Bottom**} \\ \cline{3-6}  & & **TOF (ms)** & \(E\) **(GPa)** & **TOF (ms)** & \(E\) **(GPa)** \\ \hline \multirow{4}{*}{Day 1} & & 0.59224 & 27 & 0.57640 & 37 \\  & 1 & 0.60296 & 21 & 0.58092 & 33 \\  & & 0.60428 & 21 & 0.57044 & 42 \\ \cline{2-6}  & & 0.59316 & 25 & 0.58244 & 33 \\  & 2 & 0.58156 & 33 & 0.58072 & 33 \\  & & 0.59200 & 27 & 0.57508 & 37 \\ \hline \multirow{4}{*}{Day 2} & & 0.58536 & 30 & 0.58364 & 31 \\  & 3 & 0.57764 & 35 & 0.57880 & 35 \\  & & 0.57624 & 37 & 0.57728 & 37 \\ \cline{1-1} \cline{2-6}  & & 0.57892 & 35 & 0.56896 & 45 \\ \cline{1-1}  & 4 & 0.60128 & 22 & 0.58384 & 31 \\ \cline{1-1}  & & 0.56924 & 45 & 0.58648 & 30 \\ \hline Average \(E\) (GPa) Short beam \(w/c=0.42\) & 29.83 \(\pm\) 7.08 (23.73\%) & 35.33 \(\pm\) 4.37 (12.35\%) \\ \hline Cylinder \(w/c=0.42\) & & 41.1 \(\pm\) 1.389 (3.38\%) \\ \hline Cylinder \(w/c=0.45\) & & 37.6 \(\pm\) 1.815 (4.82\%) \\ Cylinder \(w/c=0.50\) & & 31.8 \(\pm\) 1.907 (6.00\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Time of flight and modulus of elasticity of the beams in which Condition 1 was imposed. The TOF and the static modulus at the surfaces of the beams experiencing Condition 3 are summarized in Table 7. Under this scenario, 2.54 mm (0.1 in.) of water was sprinkled above the samples, whereas the bottom surface was pristine with \(w/c\) = 0.42 (see scheme of Figure 1c). It is observed that the estimated static modulus for the top surface is 31.8 GPa and it matches the cylinders with \(w/c\) = 0.50. When compared to the corresponding values presented in Tables 5 and 6 the modulus is slightly higher, and this is likely because the volume of water sprinkled on the samples was lower. Moreover, the value is much smaller than the modulus of elasticity estimated for the cylinders with \(w/c\) = 0.42. The elastic modulus measured at the bottom surface was higher than the previous two scenarios; this is expected since the specimens with Conditions 3 and 4 were not vibrated, and, therefore, it is unlikely that the water sprinkled on the top reached the bottom of the specimen. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cast Day**} & \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Top**} & \multicolumn{2}{c}{**Bottom**} \\ \cline{3-6}  & & **TOF (ms)** & \(E\) (GPa) & **TOF (ms)** & \(E\) (GPa) \\ \hline \multirow{4}{*}{Day 1} & \multirow{4}{*}{1} & 0.58332 & 31 & 0.57592 & 37 \\  & & 0.60476 & 21 & 0.57420 & 39 \\  & & 0.58260 & 31 & 0.56976 & 45 \\ \cline{2-6}  & \multirow{4}{*}{2} & 0.60224 & 22 & 0.56684 & 48 \\  & & 0.58900 & 28 & 0.58128 & 33 \\  & & 0.60460 & 21 & 0.57644 & 37 \\ \hline \multirow{4}{*}{Day 2} & \multirow{4}{*}{3} & 0.58320 & 31 & 0.59280 & 25 \\  & & 0.59096 & 27 & 0.58152 & 33 \\  & & 0.57112 & 42 & 0.57180 & 42 \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{4} & 0.57972 & 35 & 0.57800 & 35 \\  & & 0.57908 & 35 & 0.58512 & 30 \\  & & 0.58492 & 31 & 0.57236 & 42 \\ \hline Average \(E\) (GPa) Short beam \(w/c\) = 0.42 & 29.58 \(\pm\) 6.02 (20.35\%) & 37.17 \(\pm\) 6.24 (16.80\%) \\ \hline Cylinder \(w/c\) = 0.42 & \multicolumn{4}{c}{41.1 \(\pm\) 1.389 (3.38\%)} \\ \hline Cylinder \(w/c\) = 0.45 & \multicolumn{4}{c}{37.6 \(\pm\) 1.815 (4.82\%)} \\ \hline Cylinder \(w/c\) = 0.45 & \multicolumn{4}{c}{37.6 \(\pm\) 1.815 (4.82\%)} \\ \hline Cylinder \(w/c\) = 0.50 & \multicolumn{4}{c}{31.8 \(\pm\) 1.907 (6.00\%)} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Time of flight and modulus of elasticity of the beams in which Condition 2 was imposed.