Abstract
This chapter analyzes the constitutive equations of discrete electromechanical transducers. It begins with the voice coil transducer which can be used as sensor as well as actuator; it is followed by applications to modelling of the proof-mass actuator and the geophone sensor. The single axis gyrostabilizer is briefly discussed next. The second part of the chapter is devoted to the constitutive equations and the modelling of a discrete, single axis piezoelectric transducer. The physical meaning of the electromechanical coupling factor is discussed as well as its measurement. The chapter concludes with a short list of references and a set of problems.
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Notes
- 1.
The negative sign in (3.8) is irrelevant.
- 2.
Energy and coenergy functions are needed in connection with energy formulations such as Hamilton principle, Lagrange equations, or finite elements.
- 3.
Since the system is conservative, the integration can be done along any path leading from (0, 0) to \({(\varDelta ,Q)}\).
- 4.
Some damping is introduced in the system by assuming a mechanical stiffness \(K_a+cs\) instead of \(K_a\) in the mechanical part of the transducer constitutive equations (3.22)
$$ \left\{ \begin{array}{c} Q \\ f \end{array} \right\} = \left[ \begin{array}{cc} C(1-k^2) &{} \quad nd_{33}K_a \\ -nd_{33}K_a &{} \quad K_a+cs \end{array} \right] \left\{ \begin{array}{c} V \\ \varDelta \end{array} \right\} .$$
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Preumont, A. (2018). Electromagnetic and Piezoelectric Transducers. In: Vibration Control of Active Structures. Solid Mechanics and Its Applications, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-319-72296-2_3
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DOI: https://doi.org/10.1007/978-3-319-72296-2_3
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