Axisymmetric Vibration in a Submerged Piezoelectric Rod Coated with Thin Film

  • Rajendran SelvamaniEmail author
  • Farzad Ebrahimi
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Axisymmetric waves in piezoelectric rod/glass fiber Forced vibration Bessel function Actuators/sensors Thin film 


  1. 1.
    Achenbach, J.D.: Wave motion in elastic solids. Amsterdam, North-Holland (1984).zbMATHGoogle Scholar
  2. 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. 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. 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. 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).CrossRefGoogle Scholar
  6. 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).CrossRefGoogle Scholar
  7. 7.
    Graff, K.F.: Wave motion in elastic solids. Dover, Newyork (1991).zbMATHGoogle Scholar
  8. 8.
    Kim, J.O., Lee, J.G.: Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization. J. Sound Vib. 300, 241–249 (2007).CrossRefGoogle Scholar
  9. 9.
    Meeker, T.R., Meitzler, A.H.: Guided wave propagation in elongated cylinders and plates. Physical acoustics, New York Academic (1964).CrossRefGoogle Scholar
  10. 10.
    Minagawa, S.: Propagation of harmonic waves in a layered elasto-piezoelectric composite. Mech.Mater. 19, 165–170 (1995).CrossRefGoogle Scholar
  11. 11.
    Nagaya, K.: Dispersion of elastic waves in bars with polygonal cross-section. J. Acoust. Soc. Am. 70, 763–770 (1981).CrossRefGoogle Scholar
  12. 12.
    Tiersten, H.F.: Linear piezoelectric plate vibrations, New York, Plenum (1969).Google Scholar
  13. 13.
    Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988).Google Scholar
  14. 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).CrossRefGoogle Scholar
  15. 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).MathSciNetCrossRefGoogle Scholar
  16. 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. 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).CrossRefGoogle Scholar
  18. 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. 19.
    Sun, C.T., Cheng, N.C.: Piezoelectric waves on a layered cylinder. J. Appl. Phy. 45, 4288–4294 (1974).CrossRefGoogle Scholar
  20. 20.
    Wang, Q.: Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer. Int. J. Solid and Struct. 39, 3023–3037 (2002).CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsKarunya UniversityCoimbatoreIndia
  2. 2.Department of Mechanical Engineering, Faculty of EngineeringImam Khomeini International UniversityQazvinIran

Personalised recommendations