Consider a thin slab of piezoelectric element shown in Fig. 30.1. On application of a high electric field (poling field), randomly oriented dipoles get aligned to the direction of the electric field. Consequently, the strain induced is magnified. The direction of alignment is called the poling direction. Ignoring the normal stress σ_z and the shear stresses σ_xz and σ_yz for plane stress assumption, eqn. (30.4) could be further simplified as:

(30.5)

where E_p is the modulus of elasticity of the piezoelectric material, ν is the Poisson's ratio and d_ij are the piezoelectric strain-charge constants. The first three equations of (30.5) are generally used as the constitutive equations of piezoelectric actuators while the last equation is used to model piezoelectric sensors.

From eqn. (30.5), it is clear that if a piezoelectric thin slab is subjected to mechanical load, the total strain S developed in an active layer, would consist of two parts – the structural or elastic strain S_s and the piezoelectric strain S_a such that

S = Ss + Sa

(30.6)

where, S_a = [−d₃₁ E₃ , −d₃₂ E₃ , 0] ^T .

The structural strain on the other hand will depend on the nature of loading and boundary condition applied to the piezo-plate.

It is also evident from eqn. (30.5) that for poling across the lamina the active strain is developed only in the normal plane. To generate strains along the direction of the thickness of the specimen, ceramics with different crystal-cuts are used which are commonly known as Piezo-stacks. The electro elastic coupling components in the 3-3 directions, like d₃₃ or e₃₃ , become important in such cases. Another important parameter used in piezoelectricity is the voltage constant g . The higher value of g signifying higher voltage sensitivity implies more suitability of the material for sensing application. The piezoelectric constants and their significance in active vibration control are discussed in the following section.