By Rüdiger G. Ballas
The ebook describes the applying of piezoelectric fabrics, e.g. piezoceramics, within the large box of actuators and sensors. It offers a step by step creation into the constitution and mechanics of piezoelectric beam bending actuators in multilayer expertise, that are of accelerating significance for commercial functions. The dynamic behaviour of piezoelectric multilayer beam benders is defined at the foundation of the strong Lagrangian formalism and Hamiltons precept. Then follows a scientific improvement of the electromechanical circuit illustration for any type of piezoelectric beam bending actuators in the framework of community thought. diverse sensor-actuator platforms in keeping with a capacitive and an inductive sensor precept are awarded and mentioned intimately. Analytical simulations of the static and dynamic behaviour are in comparison to genuine size result of a in particular built piezoelectric multilayer beam bender. the following the suitability of the built theoretical points is proven in an excellent means.
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Extra info for Piezoelectric Multilayer Beam-Bending Actuators: Static and Dynamic Behavior and Aspects of Sensor Integration (Microtechnology and MEMS)
Example text
Above a certain temperature WF , called Curie temperature, the elementary cell of PZT provides a cube texture (see Fig. 3a). Within this crystal structure no piezoelectricity arises caused by its existing symmetry center. : A2 + : B 4+ c Ps : O 2- a a T > TC a) T < TC b) Fig. 3. Perovskit structur of ferroelectric crystals of the kind DER3 . 5 Domain and Reversion Processes of PZT 21 Falling below the Curie temperature, the cube texture of the crystal lattice turns to the tetragonal texture spontaneously due to energetic reasons [72].
44) represent a system of constitutive equations for the extensive pair of variates (T> E), the individual material constants and the constant extensive quantities can be derived from. 1 are defined [90]. 1. 46) are used for the derivation of the static behavior of a piezoelectric q-layered beam bending actuator. The fundamental base for the derivation of the dynamic behavior of a beam bending actuator is the electrical enthalpy Kh , that will be generally derived in the section below. The additional linear constitutive equations will be formulated, too.
The total thermal energy of a system caused by the kinetic energy of the ˜ of the system. This definition molecules and atoms is called internal energy X was suggested by Lord Kelvin. According to the first law of thermodynamics, the internal energy can only be changed, if energy is exchanged with the environment beyond the system borders. ˜ is equal to the sum of the supplied heat The change of the internal energy gX ˜ T and the supplied mechanical work Zp [86]. 23) ˜ and Zp show, that the amounts of supplied heat and work The terms T are infinitesimally small, however, they do not represent dierentials.