TABLE OF CONTENTS In Chapter 4 it was seen that when a piezoelectric material is placed in an electric field, the material undergoes expansion or contraction as well as shear. Which of these modes of deformation actually occurs in a particular piezoelectric material depends on the details of the piezoelectric strain matrix d given by Eq. (4-194), and the electric field vector E. However, as was seen in Example 4-3, the strains are quite small, even for a field of 1000 V/mm. Consequently the resulting displacements will also be small, unless the dimensions of the material are quite large. When piezoelectric beams are used as actuators, it is generally desirable to maximize the displacement for a given voltage. One way to increase the displacement in a piezoelectric material is to induce bending. To accomplish this, a beam is constructed of two or more layers of piezoelectric material, as shown for the two-layer case in Fig. 8-90. The layers are arranged so that the poling direction is the same for each layer, and bonded so that no slip occurs at the interface between the layers. An electric circuit is constructed so that the electric field in each layer is different. If the electric fields in the two layers have the same magnitude but are directed oppositely, one layer will expand while the other contracts. Because slip between layers is prevented, the beam will bend. Alternatively, the layers can be arranged so that the poling directions are opposite but the...
