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Elastic Waves in Generalized Thermo-Piezoelectric Transversely Isotropic Circular Bar Immersed in Fluid

Published online by Cambridge University Press:  21 December 2015

Palaniyandi Ponnusamy
Palaniyandi Ponnusamy*
Affiliation:
Department of Mathematics, Government Arts College (Autonomous), Coimbatore-641018, Tamil Nadu, India
*
*Corresponding author. Email:[email protected] (P. Ponnusamy)
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Abstract

In this paper, a mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of circular cross-sections immersed in inviscid fluid. The present study is based on the use of the three-dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied based on Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity. The frequency equations of the coupled system consisting of cylinder and fluid are developed under the assumption of perfect-slip boundary conditions at the fluid-solid interfaces, which are obtained for longitudinal and flexural modes of vibration and are studied numerically for PZT-4 material bar immersed in fluid. The computed non-dimensional frequencies are compared with Lord-Shulman, Green-Lindsay and Classical theory theories of thermo elasticity for longitudinal and flexural modes of vibrations. The dispersion curves are drawn for longitudinal and flexural modes of vibrations. Moreover, the dispersion of specific loss and damping factors are also analyzed for longitudinal and flexural modes of vibrations.

Keywords

43.40.Ey43.88.Fx43.40.Cw43.20.BiPiezoelectric cylinders/platesthermo-elasticthermal cylinder immersed in fluidsolid-fluid interactiontransversely isotropic cylinder
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 82 - 103
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Mindlin, R. D., On the equations of motion of piezoelectric crystals, in: Problems of Continuum Mechanics, SIAM, Philadelphia, N. I. Muskelishvili’s Birthday, 70 (1961), pp. 282–290.Google Scholar
[2]Mindlin, R. D., Equation of high frequency vibrations of thermo-piezoelectric, crystal plates, Interactions in Elastic Solids, Springer, Wien, 1979.Google Scholar
[3]Nowacki, W., Some general theorems of thermo-piezoelectricity, J. Thermal Stresses, 1 (1978), pp. 171–182.Google Scholar
[4]Nowacki, W., Foundations of linear piezoelectricity, in Parkus, H. (Ed.), Electromagnetic Interactions in Elastic Solids, Springer, Wien, 1979.Google Scholar
[5]Chandrasekhariah, D. S., A temperature rate dependent theory of piezoelectricity, J. Thermal Stresses, 7 (1984), pp. 293–306.Google Scholar
[6]Chandrasekhariah, D. S., A generalized linear thermoelasticity theory of piezoelectric media, Acta Mech., 71 (1988), pp. 39–49.Google Scholar
[7]Yang, J. S. and Batra, R. C., Free vibrations of a linear thermo-piezoelectric body, J. Thermal Stresses, 18 (1995), pp. 247–262.Google Scholar
[8]Sharma, J. N. and Pal, M., Propagation of Lamb waves in a transversely isotropic piezothermoelastic plate, J. Sound Vibration, 270 (2004), pp. 587–610.Google Scholar
[9]Sharma, J. N., Pal, M. and Chand, D., Three dimensional vibrational analysis of a piezothermoelastic cylindrical panel, Int. J. Eng. Sci., 42 (2004), pp. 1655–1673.CrossRefGoogle Scholar
[10]Sharma, J. N. and Walia, V., Straight and circular crested waves in generalized piezothermoelastic materials, J. Thermal Stresses, 29 (2006), pp. 529–551.Google Scholar
[11]Tang, Y. X. and Xu, K., Dynamic analysis of a piezo thermoelastic laminated plate, J. Thermal Stresses, 18 (1995), pp. 87–104.CrossRefGoogle Scholar
[12]Tauchert, T. R., Piezothermoelastic behavior of a laminated plate, J. Thermal Stresses, 15 (1992), pp. 25–37.Google Scholar
[13]Lord, H. W. and Shulman, Y., A generalized dynamical theory of thermo-elasticity, J. Mech. Phys. Solids, 5 (1967), pp. 299–309.Google Scholar
[14]Dhaliwal, R. S. and Sherief, H. H., Generalized thermo-elasticity for anisotropic media, Quarterly J. Appl. Math., 8(1) (1990), pp. 1–8.Google Scholar
[15]Green, A. E. and Laws, N., On the entropy production inequality, Arch. Rational Mech. Anal., 45 (1972), pp. 47–53.Google Scholar
[16]Green, A. E. and Lindsay, K. A., Thermo-elasticity, J. Elasticity, 2 (1972), pp. 1–7.Google Scholar
[17]Suhubi, E. S., Longitudinal vibrations of a circular cylindrical coupled with a thermal field, J. Mech. Phys. Solids, 12 (1964), pp. 69–75.Google Scholar
[18]Erbay, E. S. and Suhubi, E. S., Longitudinal wave propagation thermo-elastic cylinder, J. Thermal Stresses, 9 (1986), pp. 279–295.CrossRefGoogle Scholar
[19]Sinha, K., Plona, J., Kostek, S. and Chang, S., Axisymmetric wave propagation in a fluid-loaded cylindrical shells I: Theory; II Theory versus experiment, J. Acoust. Soc. Am., 92 (1992), pp. 1132–1155.CrossRefGoogle Scholar
[20]Berliner, J. and Solecki, R., Wave propagation in a fluid-loaded, transversely isotropic cylinders Part I. Analytical formulation; Part II Numerical results, J. Acoust. Soc. Am., 99 (1996), pp. 1841–1853.Google Scholar
[21]Guo, F. L. and Sun, R., Propagation of Bleustein-Gulyaev wave in 6mm piezoelectric materials loaded with viscous liquid, Int. J. Solid Structure, 45 (2008), pp. 3699–3710.CrossRefGoogle Scholar
[22]Qian, Z., Jin, F., Li, P. and Hirose, S., Bleustein-Gulyaev waves in 6mm piezoelectric materials loaded with a viscous layer of finite thickness, Int. J. Solid Structure, 47 (2010), pp. 3513–3518.CrossRefGoogle Scholar
[23]Venkatesan, M. and Ponnusamy, P., Wave Propagation in a solid cylinder of arbitrary cross-section immersed in a fluid, J. Acoust. Soc. Am., 112 (2002), pp. 936–942.Google Scholar
[24]Venkatesan, M. and Ponnusamy, P., Wave Propagation in a generalized thermo elastic solid cylinder of arbitrary cross-section immersed in a fluid, Int. J. Mech. Sci., 49 (2007), pp. 741–751.Google Scholar
[25]Dayal, V., Longitudinal waves in homogeneous anisotropic cylindrical bars immersed in fluid, J. Acoust. Soc. Am., 93 (1993), pp. 1249–1255.Google Scholar
[26]Nagy, B., Longitudinal guided wave propagation in a transversely isotropic rod immersed in fluid, J. Acoust. Soc. Am., 98(1) (1995), pp. 454–457.CrossRefGoogle Scholar
[27]Ahmad, F., Guided waves in a transversely isotropic cylinder immersed in fluid, J. Acoust. Soc. Am., 109(3) (2001), pp. 886–890.CrossRefGoogle Scholar
[28]Ponnusamy, P., Wave propagation in a generalized thermo elastic solid cylinder of arbitrary cross-section, Int. J. Solid Struct., 44 (2007), pp. 5336–5348.CrossRefGoogle Scholar
[29]Ponnusamy, P. and Rajagopal, M., Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid, Euro. J. Mech. A/Solid, 29 (2010), pp. 158–165.Google Scholar
[30]Ponnusamy, P., Wave propagation in thermo-elastic plate of arbitrary cross-sections, J. Multidiscipline Model. Material Structures, 7 (2011), pp. 1573–1605.Google Scholar
[31]Ponnusamy, P., Dispersion analysis of generalized thermoelastic plate of polygonal cross-sections, Appl. Math. Model., 36 (2012), pp. 3343–3358.Google Scholar
[32]Ponnusamy, P. and Selvamani, R., Dispersion analysis of generalized magneto-thermoelastic waves in a transversely isotropic cylindrical panel, J. Thermal Stresses, 35 (2012), pp. 1119–1142.CrossRefGoogle Scholar
[33]Ponnusamy, P., Wave propagation in a piezoelectric solid bar of circular cross-section immersed in fluid, Int. J. Pressure Vessels Piping, 105-106 (2013), pp. 12–18.CrossRefGoogle Scholar
[34]Paul, H. S., Vibration of circular cylindrical shells of piezo-electric silver iodide crystals, J. Acoustical Society America, 40(5) (1966), pp. 1077–1080.Google Scholar
[35]Paul, H. S. and Raju, D. P., Asymptotic analysis of the modes of wave propagation in a piezoelectric solid cylinder, J. Acoustical Society America, 71(2) (1982), pp. 255–263.Google Scholar
[36]Achenbach, J. D., Wave Motion in Elastic Solids, North-Holland, Amsterdam, 1973.Google Scholar
[37]Kolsky, H., Stress Waves in Solids, Clarendon Press, Dover, NewYork, 1963.Google Scholar
[38]Berlincourt, D. A., Curran, D. R. and Jaffe, H., Piezoelectric and Piezomagnetic Materials and Their Function in Transducers, New York and London, Academic Press, 1964.Google Scholar