On the Energy Theory of the Electromechanical Coupling Coefficient for Vibrations of Piezoelectric Bodies
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
ON THE ENERGY THEORY OF THE ELECTROMECHANICAL COUPLING COEFFICIENT FOR VIBRATIONS OF PIEZOELECTRIC BODIES V. V. Mikhailenko1 and T. V. Karnaukhova2
The electromechanical coupling coefficient (EMCC) for the vibrations of inelastic piezoelectric bodies is defined. The effect of energy dissipation is taken into account by introducing integral loss characteristic. The definition of EMCC corresponds to Ulitko’s energetic EMCC, which is interpreted as the limiting case when losses are neglected. Keywords: piezoelectric element, electromechanical coupling coefficient, reduced loss factor, circle of dimensionless conductivity Introduction. The assessment of the efficiency of electromechanical energy conversion is one of the main questions of any theory of piezoelectric bodies. The most complete characteristic of this conversion is given by integral quantities called the effective or dynamic electromechanical coupling coefficients (EMCC). Such an EMCC depends not only on the properties of the piezoelectric material, but also on the geometry of the piezoelectric element, the location of electrodes, and the vibration frequency. The approaches to determining the EMCC based on Mason’s formula [1, 4, 5] and on the energy theory developed in [3, 12] are effective. For example, the method from [6] for finding the EMCC is in full agreement with the latter theory. In connection with the expanding introduction of polymer and inelastic composite piezoelectrics, the development of EMCC theories, taking into account the inelastic behavior of a piezoelectric material, is of particular relevance [2, 10, 11]. Here, the inelastic behavior of piezoelectric material is allowed for by a direct generalization of the energy theory of EMCC to the case of harmonic vibrations of piezoelectric elements and by independently determining the EMCC taking into account losses. 1. EMCC Energy Theory: EMCCE. In [3, 12], as a characteristic of energy conversion by a piezoelectric element, it was proposed to use a quantity (hereinafter referred to as the energy EMCC : EMCCE) that is completely determined by the deformation field and the arrangement of the electrodes. Mechanical and electrical loading methods leading to a given strain state are insignificant. This idea is most simply realized in the case where the deformation and electric field strength are taken as independent variables. Then, in addition to the main problem of electroelasticity (to determine the deformation field), it is necessary to solve two additional problems for the electric potential, respectively, with open and short-circuited electrodes (to determine the internal energies in the volume of the body: U p with open-circuited electrodes; U k with short-circuited electrodes). Then the square of EMCCE is defined as: k u2 =
k2 1+ k 2
,
k2 =
U p -U k Uk
.
(1)
This expression for k u2 will be convenient below.
1
Zhytomyr Ivan Franko State University, 40 Velyka Berdychivska St., Zhytomyr, Ukraine; e-mail: vasylmikhailenko@
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