Piezoelectric Bending Transducer as an Electromechanical System
摘要
Electromechanical systems consist of interacting electrical, mechanical and acoustic subsystems that are described using circuit representations. Network theory is used to describe the overall electromechanical system in terms of a common circuit representation of the various subsystems, including their interactions. In addition to a brief introduction to the basic structure of electromechanical systems and the associated terminology, this chapter provides a systematic development of a general circuit representation of piezoelectric bending transducers. First, the concept of the ideal rod as a translational and rotational transducer is discussed. These basic considerations are followed by a description of the bending of a homogeneous beam and the associated mechanical quantities. Taking into account the mass of the differential beam element and the frictional forces occurring during its motion in the sense of equivalent viscous damping, a description of its dynamic behaviour is obtained. This results in the differential equations, which provide information about the circuit structure of a differential beam element. A limit value analysis provides a complex inhomogeneous differential equation of fourth order, the solution of which can be described in the form of an eight-terminal network linking translational and rotational flow and difference variables. The transition from the bending beam to the piezoelectric bending transducer is achieved by suitable equations of state. The electrical and mechanical quantities are coupled by means of a four-terminal network, which is combined with the previously obtained eight-terminal network, taking into account the prevailing clamping condition, and finally resulting in a circuit representation of a clamped-free bending transducer of arbitrary morphology.