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.
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References
Achenbach, J.D.: Wave motion in elastic solids. Amsterdam, North-Holland (1984).
Barshinger, J.N.: Guided waves in pipes with viscoelastic coatings. Ph.D. dissertation, The Pennsylvania State University, State College, PA (2001).
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).
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).
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).
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).
Graff, K.F.: Wave motion in elastic solids. Dover, Newyork (1991).
Kim, J.O., Lee, J.G.: Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization. J. Sound Vib. 300, 241–249 (2007).
Meeker, T.R., Meitzler, A.H.: Guided wave propagation in elongated cylinders and plates. Physical acoustics, New York Academic (1964).
Minagawa, S.: Propagation of harmonic waves in a layered elasto-piezoelectric composite. Mech.Mater. 19, 165–170 (1995).
Nagaya, K.: Dispersion of elastic waves in bars with polygonal cross-section. J. Acoust. Soc. Am. 70, 763–770 (1981).
Tiersten, H.F.: Linear piezoelectric plate vibrations, New York, Plenum (1969).
Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach, New York (1988).
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).
Selvamani, R.: Modeling of elastic waves in a fluid-loaded and immersed piezoelectric circular fiber, Int. J. Appl. Comput. Math. 3, 3263–3277 (2017).
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).
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).
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).
Sun, C.T., Cheng, N.C.: Piezoelectric waves on a layered cylinder. J. Appl. Phy. 45, 4288–4294 (1974).
Wang, Q.: Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer. Int. J. Solid and Struct. 39, 3023–3037 (2002).
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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
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DOI: https://doi.org/10.1007/978-3-030-01123-9_21
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