# Experimental Study of a Piezoelectric De-Icing System Implemented to Rotorcraft Blades
## 4 Results
### Static Direct Steady-Stade Dynamic Analysis  
Direct steady-state dynamic numerical analyses were conducted at the natural frequencies calculated using frequency analysis. Experimental icing tests were also performed with the blade setup under static (without blade rotation) mode with an ice layer accumulation for each of the modes. For each mode, the optimal actuator phasing excitation was used for numerical simulations and testing. Table 3 presents the optimal phasing for each natural mode as well as the voltage range within which delamination was predicted by the model. The piezoelectric actuators attached to the inside upper surface of the profile from left to right are identified as 1 to 3, while the actuator patches, from left to right, attached to the inside of the lower surface of the profile were identified as 4 to 6 (Figures 4 and 5). Actuators on the same side of the backslash are all excited identically, at the same voltage and in phase. However, they are excited, at the same voltage, and in counter phase with the actuators on the other side of the backslash. The ice delamination is predicted to be achieved when the calculated numerical shearing stress values at the ice substrate interface are within the yield limit range defined during experiments with the flat plate and validated in the literature, as detailed in [19]. The voltage range corresponds to the voltage required to achieve the stress range defined previously. As explained in Section 2.3, a maximum of 500 Vpp can be applied without compromising the integrity of the actuators when not all the actuators are excited in phase. Testing was conducted by performing a frequency sweep at a low sweep rate (below 70 Hz/s) around the target frequencies and slightly increasing the voltage between each sweep until delamination was obtained or maximum voltage was reached. Delamination was obtained experimentally when the structure was excited using the actuator patches for modes 5 and 6, as presented in Table 3, while mode 3 could not be excited due to the form of the mode shape and the disposition of the piezoelectric patches. Figure 7: Resonant mode: (**a**) mode 7 at 2487 Hz and (**b**) mode 12 at 3340 Hz and position of the actuator patch circled in red (**top**) and highlighted (**bottom**) positioned on two different anti-nodes. For the third mode, the optimal actuator excitation is defined by all in-phase actuators (Figure 6c). With this activation, the numerical model results showed that the piezoelectric actuators would not properly excite the structure. As expected, the mode deployment only partially corresponds to the third resonant mode shape (Figure 8) but is largely affected by the geometrical disposition of the patches. The piezoelectric d\({}_{31}\) effect, which represents the directions of the mechanical strain experienced by the actuator from the application of an electric field, creates a deformation of the actuators in both directions, as shown in Figure 9. With the greater deformation generated over the length, the actuators at the center create more of an anti-node corresponding to that of the middle anti-node of mode 5. If the actuators were positioned in the perpendicular direction, their deformation would have favored bending, mostly in the direction proper to mode 3 generation. However, due to size restrictions, it was not possible to accommodate the patches positioning. This demonstrates that, experimentally, while mode 5 could be excited, mode 3 would not. This was also confirmed experimentally since no distinct resonant mode was observed around the natural frequency corresponding to the third mode, only for mode 5.