Engineering Transactions, 66, 3, pp. 211–227, 2018
10.24423/EngTrans.859.20180726

Influence of Rotation on Transversely Isotropic Piezoelectric Rod Coated with a Thin Film

Rajendran SELVAMANI
Karunya University
India

Oluwole Daniel MAKINDE
Stellenbosch University
South Africa

In this paper, the influence of rotation on axisymmetric waves of a piezoelectric rod coated with a thin film is studied using constitutive form linear theory elasticity and piezo-electric equations. Potential functions are introduced to uncouple the equations of motion in radial and axial directions. The surface area of the rod is coated by a perfectly conducting material. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied numerically for PZT-4 ceramics. The computed non-dimensional frequency, phase velocity, relative frequency shift, electromechanical coupling and electric displacement are presented in the form of dispersion curves. This type of study is important in the construction of
rotating sensors and gyroscope.
Keywords: wave propagation in piezoelectric cylinder/fiber; forced vibration; Bessel function; actuators/sensors; thin film
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Graff K.F., Wave Motion in Elastic Solids, Dover, New York, 1991.

Achenbach J.D., Wave Motion in Elastic Solids, Amsterdam, North-Holland, 1984.

Meeker T,R., Meitzler A.H., Guided wave propagation in elongated cylinders and plates, in: Physical Acoustics: Principles and Methods, Warren P. Mason [Ed.], pp. 111–166, Academic Press, New York-London, 1964.

Honarvar F., Enjilela E., Sinclair A.N., Mirnezami A.S., Wave propagation in transversely isotropic cylinders, International Journal of Solids and Structures, 44(16): 5236–5246, 2007.

Wang Y., Hao H., Modelling of guided wave propagation with spectral element: application in structural engineering, Applied Mechanics and Materials, 553: 687–692, 2014.

Tiersten H.F., Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969.

Parton V.Z., Kudryavtsev B.A., Electromagnetoelasticity, Gordon and Breach Science Publishers, New York, 1988.

Paul H.S., Venkatesan M., Wave propagation in a piezoelectric ceramic cylinder of arbitrary cross section, The Journal of the Acoustical Society of America, 82(6): 2013–2020, 1987.

Nagaya K., Dispersion of elastic waves in bars with polygonal cross-section, The Journal of the Acoustical Society of America, 70 (3): 763–770, 1981.

Ebenezer D.D., Ramesh R., Analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on flat surfaces, The Journal of the Acoustical Society of America, 113(4): 1900–1908, 2003.

Botta F., Cerri G., Wave propagation in Reissner-Mindlin piezoelectric coupled cylinder with non-constant electric field through the thickness, International Journal of Solids and Structures, 44 (18–19): 6201–6219, 2007.

Kim J.O., Lee J.G., Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization, Journal of Sound and Vibration, 300 (1-2): 241–249, 2007.

Selvamani R., Modeling of elastic waves in a fluid-loaded and immersed piezoelectric circular fiber, International Journal of Applied and Computational Mathematics, 3(4): 3263–3277, 2017.

Rao C.K., Rao L.B., Nonlocal critical velocities of fluid conveying clamped-pinned single-walled carbon nanotubes subjected to axial magnetic field, Engineering Transactions, 65(2): 319–333, 2017.

Abd-Alla A.M., Bayones F.S., Effect of rotation in a generalized magneto thermo viscoelastic media, Advances in Theoretical and Applied Mechanics, 4: 15–42, 2011.

Wauer J., Waves in rotating and conducting piezoelectric media, The Journal of the Acoustical Society of America, 106(2): 626–636, 1999.

Roychoudhuri S.K., Mukhopadhyay S., Effect of rotation and relaxation times on plane waves in generalized thermo-visco-elasticity, International Journal of Mathematics and Mathematical Sciences, 23(7): 497–505, 2000.

Dragomir S.C.,Sinnott M.D.., Eren Semercigil S., Turan Ö.F., A study of energy dissipation and critical speed of granular flow in a rotating cylinder, Journal of Sound and Vibration, 333(25): 6815–6827, 2014.

Bayat M., Rahimi M., Saleem M., Mohazzab A.H., Wudtke I., Talebi H., One-dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk, Applied Mathematical Modelling, 38(19-20): 4625–4639, 2014.

Selvamani R., Ponnusamy P., Effect of rotation in an axisymmetric vibration of a transversely isotropic solid bar immersed in an inviscid fluid, Material Physics and Mechanics, 15: 97–106, 2012.

Selvamani R., Ponnusamy P., Wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section, Multidiscipline Modeling in Materials and Structures, 11(2): 216–237, 2015.

Dai H.-H, Kaplunov J., Prikazchikov D.A., A long-wave model for the surface elastic wave in a coated half-space, Proceeding of Royal Society A, 466 (2122): 3097–3116, 2010.

Wang Q., Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer, International Journal of Solids and Structures, 39 (11): 3023–3037, 2002.

Sun C.T., Cheng N.C., Piezoelectric waves on a layered cylinder, Journal of Applied Physics, 45: 4288–4294, 1974.

Minagawa S., Propagation of harmonic waves in a layered elasto-piezoelectric composite, Mechanics of Materials, 19 (2–3): 165–170, 1995.

Camassa R., Ogrosky H.R., On viscous film flows coating the interior of a tube: thin-film and long-wave models, Journal of Fluid Mechanics, 772: 569–599, 2015.

Barshinger J.N., Guided waves in pipes with viscoelastic coatings, Ph.D. Dissertation, The Pennsylvania State University, PA, 2001.

Park K.I., Xu S., Liu Y., Hwang G.T., Kang S.J.,Wang Z.L., Lee K.J., Piezoelectric BaTiO3 thin film nanogenerator on plastic substrates, Nano Letters, 10(12): 4939–4943, 2010.

Berlincourt D.A., Curran D.R., Jaffe H., Piezoelectric and piezomagnetic materials and their function in transducers, in: Physical Acoustics: Principles and Methods, Warren P. Mason (Ed.),pp.169-267, Academic Press, New York – London, 1964.




DOI: 10.24423/EngTrans.859.20180726