Skip to main content

Axisymmetric Vibration in a Submerged Piezoelectric Rod Coated with Thin Film

  • Conference paper
  • First Online:
Applied Mathematics and Scientific Computing

Part of the book series: Trends in Mathematics ((TM))

  • 629 Accesses

Abstract

This paper is concerned with the axisymmetric elastic waves in a transversely isotropic submerged piezoelectric rod coated with thin film using a constitutive form of linear theory of elasticity and piezoelectric equations. The equations of motion along radial and axial directions are decoupled by using potential functions. The surface area of the rod is coated by a perfectly conducting material, and no slip boundary condition is employed along the solid-fluid interactions. The dispersion equation which contains the longitudinal and flexural modes is derived and is studied numerically. To observe the variations of mechanical and electric displacement in the coated piezoelectric rod, the authors compute the numerical values of the field variables for the ceramic PZT − 4. The effects of fluid and coating environment on the variation of field variables are analyzed and presented graphically. This type of study is important in the modeling of underwater sensors for the navigation applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Achenbach, J.D.: Wave motion in elastic solids. Amsterdam, North-Holland (1984).

    MATH  Google Scholar 

  2. Barshinger, J.N.: Guided waves in pipes with viscoelastic coatings. Ph.D. dissertation, The Pennsylvania State University, State College, PA (2001).

    Google Scholar 

  3. Berliner, J., Solecki, R.: Wave Propagation in a fluid-loaded transversely isotropic cylinder. Part I. Analytical formulation; Part II Numerical results, J. Acoust. Soc. Am. 99, 1841–1853 (1996).

    Google Scholar 

  4. Berlin Court, D.A., Curran, D.R., Jaffe, H.: Piezoelectric and piezomagnetic materials and their function in transducers. Physical Acoustics, 1A (W.P.Mason, editor), Academic Press, New York and London (1964).

    Google Scholar 

  5. Botta, F., Cerri, G.: Wave propagation in Reissner-Mindlin piezoelectric coupled cylinder with non-constant electric field through the thickness. Int. J. Solid and Struct. 44, 6201–6219 (2007).

    Article  Google Scholar 

  6. Ebenezer, D.D., Ramesh, R.: Analysis of axially polarized piezoelectric cylinders with arbitrary boundary conditions on the flat surfaces. J. Acoust. Soc. Am. 113(4), 1900–1908 (2003).

    Article  Google Scholar 

  7. Graff, K.F.: Wave motion in elastic solids. Dover, Newyork (1991).

    MATH  Google Scholar 

  8. Kim, J.O., Lee, J.G.: Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization. J. Sound Vib. 300, 241–249 (2007).

    Article  Google Scholar 

  9. Meeker, T.R., Meitzler, A.H.: Guided wave propagation in elongated cylinders and plates. Physical acoustics, New York Academic (1964).

    Book  Google Scholar 

  10. Minagawa, S.: Propagation of harmonic waves in a layered elasto-piezoelectric composite. Mech.Mater. 19, 165–170 (1995).

    Article  Google Scholar 

  11. Nagaya, K.: Dispersion of elastic waves in bars with polygonal cross-section. J. Acoust. Soc. Am. 70, 763–770 (1981).

    Article  Google Scholar 

  12. Tiersten, H.F.: Linear piezoelectric plate vibrations, New York, Plenum (1969).

    Google Scholar 

  13. Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988).

    Google Scholar 

  14. Paul, H.S., Venkatesan, M.: Wave propagation in a piezoelectric ceramic cylinder of arbitrary cross section. J. Acoust. Soc. Am. 82(6), 2013–2020 (1987).

    Article  Google Scholar 

  15. Selvamani, R.: Modeling of elastic waves in a fluid-loaded and immersed piezoelectric circular fiber, Int. J. Appl. Comput. Math. 3, 3263–3277 (2017).

    Article  MathSciNet  Google Scholar 

  16. Selvamani, R., Ponnusamy, P.: Effect of rotation in an axisymmetric vibration of a transversely isotropic solid bar immersed in an inviscid fluid. Mater. Phys. Mechs. 15, 97–106 (2012).

    Google Scholar 

  17. Selvamani, R., Ponnusamy, P.: Wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section. Multidi. Model. Mater. Struct. 11(2), 216–237 (2015).

    Article  Google Scholar 

  18. Sinha, K., Plona, J., Kostek, S., Chang, S.: Axisymmetric wave propagation in a fluid-loaded cylindrical shell. I: Theory; II Theory versus experiment. J. Acoust. Soc. Am. 92, 1132–1155 (1992).

    Google Scholar 

  19. Sun, C.T., Cheng, N.C.: Piezoelectric waves on a layered cylinder. J. Appl. Phy. 45, 4288–4294 (1974).

    Article  Google Scholar 

  20. Wang, Q.: Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer. Int. J. Solid and Struct. 39, 3023–3037 (2002).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rajendran Selvamani .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Selvamani, R., Ebrahimi, F. (2019). Axisymmetric Vibration in a Submerged Piezoelectric Rod Coated with Thin Film. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_21

Download citation

Publish with us

Policies and ethics