## 3 Static/Dynamic Response Characteristics of IEPCM  
### Static Response Analysis of IEPCM  
Here, the ratio of the transverse stress and strain of the IEPCM in the \(y\)-axis to the corresponding longitudinal ones in the \(x\)-axis are focused on. The static stress and strain distributions in the \(x\)- and \(y\)-direction of the IEPCM are shown in Figure 2a,b and Figure 3a,b.  
The maximum stress in the \(x\)-direction was 3.41 MPa, and it appeared on both ends of the IEPCM as shown in Figure 2a,b. Moreover, most of the stresses were about 0.704 MPa. The maximum stress in the \(y\)-direction was 1.31 MPa, and it also appeared on both ends of the IEPCM. Obviously, the corresponding IEPCM showed different driving stress responses in the transverse and longitudinal directions. As can be seen from Figure 3a,b, the maximum strain of the IEPCM in the \(x\)-direction was 6.07 \(\mu\varepsilon\), and it appeared on both ends. In the middle region, the strain from the left to right sides between neighboring electrodes was altered  
Figure 2: Static stress distributions of IEPCM under applied 10 V voltage: (a) \(x\)-direction; (b) \(y\)-direction.  
from a high to low value, and the maximum value was 2.47 \(\mu\epsilon\). The maximum strain in the \(y\)-direction was 0.918 \(\mu\epsilon\), also appearing on both ends. In the middle region, the strain from the upper and lower sides between neighboring electrodes was also altered from a high to low value, and the maximum strain value was 1.16 \(\mu\epsilon\). The maximum strain ratio in the \(x\)-, \(y\)-direction at both ends, and in the middle region of the IEPCM, was 3.19, 2.69, respectively. It shows that there is a great difference between the transverse and the longitudinal strain, which presents an obvious orthotropic characteristic and can effectively meet the basic requirements of engineering needs as well.  
Through numerical analysis of half the local area between a pair of opposite electrodes of an interdigitated piezoelectric element, [PERSON] et al. found that there are quite different results between the full model and local area because the latter ignored the influence from the other part [24]. Here, a numerical simulation on the static analysis between neighboring electrodes of the IEPCM was also studied in order to compare the difference between the full model and local area.  
The static analysis results show that the maximum stress in the \(x\)- and \(y\)-direction in the full model were both about three times larger than those in local area just between neighboring electrodes, which shows that the size change in the \(x\)-direction has a significant influence on the stress distributions in the \(x\)- or \(y\)-direction. However, the maximum strain in the \(x\)- and \(y\)-direction in the full model are just 6.59%, 1.04% larger than that between neighboring electrodes, respectively, which indicates that the size change in the \(x\)-direction has little influence on the strain distributions in the \(x\)- and \(y\)-direction.  
Therefore, during the next numerical analysis and optimal design of the IEPCM, in order to reduce the simulation time under the prerequisite of ensuring good quality and enhance the calculation efficiency, the full model of the IEPCM is simplified into the local area between neighboring electrodes. Supposing the driving strains in the \(x\)-direction are the state variables, the optimal results for the control variables \(W\), \(P\), and the thickness of \(H\) can be acquired.