Abstract
In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic waves.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Al-Qahtani H., Datta S.: Thermoelastic waves in an anisotropic infinite plate. J. Appl. Phys. 96, 3645–3658 (2004)
Nayfeh A.H., Nemat-Nasser S.: Thermoelastic waves in solids with thermal relaxations. Acta Mech. 12, 53–69 (1971)
Sinha H., Sinha S.B.: Velocity of Rayleigh waves with thermal relaxation in time. Acta Mech. 23, 159–166 (1975)
Sherief H.H., Helmy K.A.: A two-dimensional generalized thermoelasticity problem for a half space. J. Therm. Stress. 22, 897–910 (1999)
Abd-alla A.E.N., Al-dawy A.A.S.: Thermal relaxation times effect on Rayleigh waves in generalized thermoelastic media. J. Therm. Stress. 24, 367–381 (2001)
Massalas C.V.: Thermoelastic waves in a thin plate. Acta Mech. 65, 51–61 (1986)
Daimaruya M., Naitoh M.: Dispersion and energy dissipation of thermoelastic waves in a plate. J. Sound Vib. 117, 511–518 (1987)
Massalas C.V., Kalpakidis V.K.: Thermoelastic waves in a waveguide. Int. J. Eng. Sci. 25, 1207–1218 (1987)
Sharma J.N., Singh D., Kumar R.: Generalized thermoelastic waves in homogeneous isotropic plates. J. Acoust. Soc. Am. 108, 848–851 (2000)
Verma K.L., Hasebe N.: Dispersion of thermoelastic waves in a plate with and without energy dissipation. Int. J. Thermophys. 22(3), 957–978 (2001)
Verma K.L., Hasebe N.: Wave propagation in plates of general anisotropic media in generalized thermoelasticity. Int. J. Eng. Sci. 39, 1739–1763 (2001)
Verma K.L., Hasebe N.: Wave propagation in transversely isotropic plates in generalized thermoelasticity. Arch. Appl. Mech. 72, 470–482 (2002)
Rajneesh K., Tarun K.: Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. Int. J. Solids Struct. 45, 5890–5913 (2008)
Rajneesh, K., Tarun, K.: Rayleigh-LambWaves in transversely isotropic thermoelastic diffusive layer. Int. J. Thermophys. doi:10.1007/s10765-008-0522-x
Al-Qahtani, H.: Extensional thermoelastic waves in transversely isotropic plate according to a higher order theory. Acta Mech. doi:10.1007/s00707-008-0130-7
Hawwa M.A., Nayfeh A.H.: The general problem of thermoelastic waves in anisotropic periodically laminated composites. Compos. Eng. 5(12), 1499–1517 (1995)
Hawwa M.A., Nayfeh A.H.: Thermoelastic waves in a laminated composite with a second sound effect. J. Appl. Phys. 80(5), 2733–2738 (1996)
Verma K.L.: On the propagation of waves in layered anisotropic media in generalized thermoelasticity. Int. J. Eng. Sci. 40, 2077–2096 (2002)
Ponnusamy P.: Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section. Int. J. Solids Struct. 44, 5336–5348 (2007)
Sharma J.N., Pathania V.: Generalized thermoelastic wave propagation in circumferential direction of transversely isotropic cylindrical curved plates. J. Sound Vib. 281, 1117–1131 (2005)
Brekhovskikh L.M.: Surface waves confined to the curvature of the boundary in solid. Sov. Phys. Acoust. 13, 462–472 (1968)
Shah A.H., Ramakrishnan C.V., Datta S.K.: Three-dimensional and shell-theory analysis of elastic waves in a hollow sphere. ASME J. Appl. Mech. 36, 431–439 (1969)
Gaunaurd G.C., Werby M.F.: Similarities between various Lamb waves in submerged spherical shells, and Rayleigh waves in elastic spheres and flat half-spaces. J. Acoust. Soc. Am. 89, 2731–2739 (1991)
Gaunaurd G.C., Werby M.F.: Sound scattering by resonantly excited, fluid loaded, elastic spherical shells. J. Acoust. Soc. Am. 90, 2536–2550 (1991)
Kargl S.G., Marston P.L.: Ray synthesis of lamb wave contributions to the total scattering cross section for an elastic spherical shell. J. Acoust. Soc. Am. 88, 1103–1113 (1990)
Wang X., Lu G., Guillow S.R.: Stress wave propagation in orthotropic laminated thick-walled spherical shells. Int. J. Solids Struct. 39, 4027–4037 (2002)
Towfighi S., Kundu T.: Elastic wave propagation in anisotropic spherical curved plates. Int. J. Solids Struct. 40, 5495–5510 (2003)
Yu J.G., Wu B., Huo H.L., He C.F.: Characteristics of guided waves in anisotropic spherical curved plates. Wave Motion 44(4), 271–281 (2007)
Yu J.G., Wu B., Huo H.L., He C.F.: Wave propagation in functionally graded piezoelectric spherical curved plates. Phys. Status Solidi (b) 244(9), 3377–3389 (2007)
Lefebvre J.E., Zhang V., Gazalet J., Gryba T.: Legendre polynomial approach for modeling free-ultrasonic waves in multilayered plates. J. Appl. Phys. 85, 3419–3427 (1999)
Jiangong Y., Qiujuan M.: Circumferential wave in functionally graded piezoelectric cylindrical curved plates. Acta Mech. 198(3–4), 171–190 (2008)
Yu J.G., Wu B., He C.F.: Characteristics of guided waves in graded spherical curved plates. Int. J. Solids Struct. 44(11–12), 3627–3637 (2007)
Wu B., Yu J.G., He C.F.: Wave propagation in non-homogeneous magneto-electro-elasitc plates. J. Sound Vib. 317(1–2), 250–264 (2008)
Yu J.G., Wu B.: Circumferential wave in magneto-electro-elastic functionally graded cylindrical curved plates. Eur. J. Mech. A/Solids 28(3), 560–568 (2009)
Jiangong Y., Bin W.: Chen Guoqiang. Wave characteristics in functionally graded piezoelectric hollow cylinders. Arch. Appl. Mech. 79(9), 807–824 (2009)
Sharma J.N., Pathania V.: Generalized thermoelastic waves in anisotropic plates sandwiched between liquid layers. J. Sound Vib. 278(1–2), 383–411 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiangong, Y., Tonglong, X. Generalized thermoelastic waves in spherical curved plates without energy dissipation. Acta Mech 212, 39–50 (2010). https://doi.org/10.1007/s00707-009-0238-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-009-0238-4