Based on the differential equation for bending waves in the previous chapter, this chapter investigates the dynamic behaviour of piezoelectric bending transducers. The question is how the energetic conjugates torsional displacement \(\varphi \) , displacement w, volume displacement V, charge displacement Q can be represented as functions of time t (dynamics) and the length coordinate x in the case of harmonic excitation with loads (moment M, force F, pressure p, electric voltage U). The answer to this question allows, on the one hand, an analytical approach to the description of the vibration behaviour and, on the other hand, provides a deeper understanding when determining a circuit representation of piezoelectric bending transducers as an electromechanical system in the next chapter.

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Dynamic Behaviour of Piezoelectric Bending Transducers

  • Rüdiger G. Ballas

摘要

Based on the differential equation for bending waves in the previous chapter, this chapter investigates the dynamic behaviour of piezoelectric bending transducers. The question is how the energetic conjugates torsional displacement \(\varphi \) , displacement w, volume displacement V, charge displacement Q can be represented as functions of time t (dynamics) and the length coordinate x in the case of harmonic excitation with loads (moment M, force F, pressure p, electric voltage U). The answer to this question allows, on the one hand, an analytical approach to the description of the vibration behaviour and, on the other hand, provides a deeper understanding when determining a circuit representation of piezoelectric bending transducers as an electromechanical system in the next chapter.