# Effect of Ultrasonic Vibration on the Surface Adhesive Characteristic of Iced Aluminum Alloy Plate
## 3 Effect of PZT Patch Size on Shear Stress
### The Effect of Side Length
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Side Length of PZT Patch/mm** & **Excitation Frequency/kHz** & **Maximum Shear Stress/Pa** \\ \hline
16 & 59 & 2.76 \(\times\) 10\({}^{6}\) \\
16 & 87 & 8.69 \(\times\) 10\({}^{6}\) \\
14 & 79 & 7.83 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters and maximum shear stresses. Figure 7: Variations in maximum shear stress with excitation frequency and the side length of the PZT patch. As shown in Figure 8a, when the side length of the PZT patch is 14 mm \(\times\) 14 mm, and the vibration frequency is 79 kHz, the shear stress, whose absolute value is greater than the adhesive shear stress of ice, distributes in a local, small area. The shear stresses alternate positively and negatively. In this case, ultrasonic vibration can reduce the adhesive force of most parts of the ice covering on the whole adhesive interface. Similarly, as shown in Figure 8b, when the side length of the PZT patch is 16 mm \(\times\) 16 mm, and the vibration frequency is 87 kHz, the shear stress satisfying deicing conditions mainly concentrates in the four corners of the iced aluminum alloy plate. In this case, the areas in these regions are large, and the ultrasonic vibration can reduce the adhesive force of the ice near the corners of the iced aluminum alloy plate. As shown in Figure 8c, when vibration frequency is 59 kHz, the shear stresses satisfying the deicing condition are located in the center of the interface, and their areas are all small. In this case, ultrasonic vibration can reduce the adhesive force of the ice near the center of the iced aluminum alloy plate. In the above cases, although there are some areas whose shear stresses satisfy the deicing condition, there are some areas whose shear stresses are still lower. These areas degrade the deicing effect of the ultrasonic vibration. To quantitatively assess the ratio of the area with a shear stress value satisfying deicing conditions to the whole interface, a definition of one parameter \(P\), named deicing area ratio, was proposed, which is the ratio of the areas whose shear stress at the adhesive interface are greater than the adhesive shear stress of ice to the whole adhesive interface area. Its mathematical expression is defined in the following Equation (4):  
\[P=\frac{S_{1}}{S} \tag{4}\]  
where \(P\) is the deicing area ratio; \(S_{1}\) is total areas whose shear stresses at the adhesive interface are greater than the adhesive shear stress of the ice; \(S\) is the adhesive interface area. Based on the above calculation results, the values of the deicing area ratios under the different side lengths of the PZT patches are calculated by Equation (4), and the results are shown in Figure 9.  
As shown in Figure 9, when the side length of the PZT patch is 16 mm \(\times\) 16 mm, and the vibration frequency is 87 kHz, the deicing area ratio is highest, and the value is 0.59. When the side length of the PZT patch is 14 mm \(\times\) 14 mm, and the vibration frequency is 79 kHz, the deicing area ratio is 0.58. The areas are approximately equal under these two conditions. In contrast, when the side length of the PZT patch is 16 mm \(\times\) 16 mm, and the excitation frequency is 59 kHz, the deicing area ratio is very small, and its value is 0.074. These results show that there is an optimum side length for the PZT patch, as the size of  
Figure 8: Distributions of shear stress at the adhesive interface: (**a**) side length is 14 mm, and frequency is 79 kHz; (**b**) side length is 16 mm, and frequency is 87 kHz; (**c**) side length is 16 mm, and frequency is 59 kHz. an iced plate is constant. In this case, the deicing area ratio is highest, and the ultrasonic vibration deicing affecting the reduction in the adhesive force of ice is significant. The reason for this result is that when the side length of the PZT patch is short, the output power of the PZT patch is low, and the bending deformation of the iced aluminum alloy plate excited by the PZT patch is small.