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Radial vibrations of composite piezoelectric ceramic disks

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Abstract

A theory is developed for the radial vibrations of thin disks composed of several piezoelectric ceramic materials bonded at their cylindrical interfaces. Closed type solutions are obtained for the resonant and antiresonant frequency equations, and numerical results are presented for various steel/PZT-4 composite disks. The frequency spectrums and corresponding electromechanical coupling factors are found to be quite sensitive to the heterogeneity of the considered piezoelectric systems.

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Abbreviations

a kl ,A (i),b k ,B (i) :

constants

c kl :

elastic moduli at constant electric field

c 11,c 12 :

modified elastic moduli defined by (2.4.1) and (2.4.2)

D k :

electric displacement vector

e kl :

piezoelectric constants

e 31 :

modified piezoelectric constant defined by (2.4.3)

f (1)a ,f (1)r :

fundamental antiresonant and resonant frequencies

h :

half-thickness of disk

i :

index referencing regioni of the composite disk

J 0,J 1,Y 0,Y 1 :

Bessel functions

k p :

electromechanical coupling factor defined by (3.4)

n :

number of composite regions

r, θ, z :

cylindrical coordinates

t :

time, thickness

T kl :

stress tensor

u k :

mechanical displacement vector

v :

phase velocity defined by (2.8)

ɛ kl :

permittivity components at constant strain

ε 33 :

modified permittivity component defined by (2.4.4)

ρ :

mass density

σ p :

Poisson's ratio defined by (3.2)

φ :

electric potential

ω :

circular frequency, 2πf

ω a,ω r :

antiresonant and resonant circular frequencies

References

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  5. Meitzler, A. H., H. M. O'Bryan, Jr. andH. F. Tiersten, IEEE Trans. Sonics and UltrasonicsSU-20 (1973) 233.

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  6. Mason, W. P., Ed., Physical Acoustics, Vol. I Part A, Academic Press, N.Y., 1964, Chapter 3.

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Authors and Affiliations

  1. Department of Mechanics, Technion — Israel Institute of Technology, Haifa, Israel

    Yehuda Stavsky & Nachman T. Adelman

Authors
  1. Yehuda Stavsky
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  2. Nachman T. Adelman
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Stavsky, Y., Adelman, N.T. Radial vibrations of composite piezoelectric ceramic disks. Appl. Sci. Res. 31, 123–138 (1975). https://doi.org/10.1007/BF01795831

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  • DOI: https://doi.org/10.1007/BF01795831

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