Theory of the Dynamic Behavior of Piezoelectric Beam Bending Actuators

Abstract

In the previous chapter, the energy density of the elastic deformation and the electrical energy density of a solid body have been described and derived. They provide a basis for the description of the deformation and stress state of piezoelectric materials within the scope of thermodynamics. This approach directly results in the piezoelectric constitutive equations being essential for the description of the static behavior of piezoelectric multilayer beam bend-ing actuators. With respect to the constitutive equations, the consideration of the crystal symmetry of PZT provides a basis for the description of the static behavior of n-layered beam benders. The extensive state variables (T, E) are the starting point for the static behavior modeling. In combination with the linear piezoelectric constitutive equations, the total stored energy of the bend-ing actuator can be formulated. The theorem of minimum total potential energy provides the combination of the extensive parameters such as mechanical moment M , force F , pressure load p and driving voltage U with the intensive parameters angular deflection α, deflection ξ, volume displacement V and the electric charge Q as functions of any point x over the entire length of the bending actuator.