**2. Piezoelectric effects**

Piezoelectric materials are kind of crystals that have no inversion symmetry structures. As is known to all, under an external electric field, piezoelectric materials can generate deformations because of the rotation of the internal electric domain. When it comes to piezoelectric materials, piezoelectric effects are the most special functional characteristics including the direct piezoelectric effect and the converse piezoelectric effect [31–34]. When the mechanical stress is applied to the piezoelectric materials, electric charges can be produced on the electrodes of the piezoelectric materials, which is called the direct piezoelectric effect. Conversely, when electric voltages are applied on the electrodes of the piezoelectric materials, mechanical deformations can be generated on the piezoelectric materials, which is called the converse piezoelectric effect [33, 34]. In a real application, using the direct piezoelectric effect, piezoelectric materials can be employed as sensors. Using the converse piezoelectric effect, piezoelectric materials can be employed as actuators [33, 34].

PZT (Pb (ZrxTi1 − *x*)O3) is a kind of piezoelectric ceramic material with excellent performance which has been used widely. Usually, PZT can be manufactured to be sheet, circular, ring, block, and so on. For the piezoelectric materials, there are three key parameters influencing the piezoelectric effects: the output strain *δ*, polarization field *P,* and actuation field *E*. According to the orientations of the three key parameters, the piezoelectric actuators can function in three working modes: longitudinal mode, transversal mode, and shear mode [35, 36]. As **Figure 2(a)** shows, in the manufacturing process, a block of piezoelectric material is polarized and the polarization field is *P*. The coordinate system on the piezoelectric material is established and the six-coordinate axes are named *x* (1), *y* (2), *z* (3), *θ*x (4), *θ*y (5) and *θ*<sup>z</sup>

**Figure 2.**

*Converse piezoelectric effect [32]. (a) Actuation and polarization fields; (b) longitudinal and transversal modes; (c) shear mode.*

(6), respectively. The electric field *E* is applied to actuate the piezoelectric material. If the actuation field *E* and the polarization field *P* have the same direction or the opposite direction, deformations from the longitudinal direction and the transversal direction are generated simultaneously, which are named *δ*h and *δ*l, respectively. Correspondingly, these are the longitudinal mode and transversal mode of the piezoelectric material, respectively (see **Figure 2(b)**). If the actuation field *E* and the polarization field *P* have the vertical directions, deformation from the shear direction is generated, which is named *δ*s. This is the shear mode of the piezoelectric material (see **Figure 2(c)**) [35, 36].
