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Original Articles

Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere

Pages 265-276 | Received 30 May 2014, Accepted 16 Aug 2014, Published online: 04 Mar 2015

REFERENCES

  • Abbas , I. ( 2006 ). Natural frequencies of a poroelastic hollow cylinder . Acta Mechanica 186 ( 1–4 ): 229 – 237 .
  • Abbas , I. ( 2009 ). Generalized magneto-thermoelasticity in a nonhomogeneous isotropic hollow cylinder using the finite element method . Archive of Applied Mechanics 79 ( 1 ): 41 – 50 .
  • Abbas , I. A. ( 2013 ). A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole . Applied Mathematics Letters 26 ( 2 ): 232 – 239 .
  • Abbas , I. A. ( 2014 ). Three-phase lag model on thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a cylindrical cavity . Journal of Computational and Theoretical Nanoscience 11 ( 4 ): 987 – 992 .
  • Abbas , I. A. , Othman , M. I. A. (2012). Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli. Chinese Physics B 21(1):014601.
  • Abbas , I. A. , Youssef , H. M. ( 2012 ). A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method . International Journal of Thermophysics 33 ( 7 ): 1302 – 1313 .
  • Abbas , I. A. , Zenkour , A. M. ( 2013 ). LS model on electro-magneto-thermoelastic response of an infinite functionally graded cylinder . Composite Structures 96 : 89 – 96 .
  • Abd-alla , A. N. , Abbas , I. ( 2002a ). A problem of generalized magnetothermo-elasticity for an infinitely long, perfectly conducting cylinder . Journal of Thermal Stresses 25 ( 11 ): 1009 – 1025 .
  • Abd-alla , A. N. , Abbas , I. A. A. ( 2002b ). Magnetoelastic longitudinal wave propagation in a transversely isotropic circular cylinder . Applied Mathematics and Computation 127 ( 2–3 ): 347 – 360 .
  • Cuyt , A. , Petersen , V. B. , Verdonk , B. , Waadeland , H. , Jones , W. B. ( 2008 ). Handbook of Continued Fractions for Special Functions . New York : Springer .
  • Das , N. C. , Lahiri , A. , Giri , R. R. ( 1997 ). Eigenvalue approach to generalized thermoelasticity . Indian Journal of Pure and Applied Mathematics 28 ( 12 ): 1573 – 1594 .
  • Dhaliwal , R. S. , Sherief , H. H. ( 1980 ). Generalized thermoelasticity for anisotropic media . Quarterly of Applied Mathematics 38 ( 1 ): 1 – 8 .
  • Elhagary , M. A. ( 2011 ). Generalized thermoelastic diffusion problem for an infinitely long hollow cylinder for short times . Acta Mechanica 218 ( 3–4 ): 205 – 215 .
  • Elhagary , M. A. ( 2012 ). Generalized thermoelastic diffusion problem for an infinite medium with a spherical cavity . International Journal of Thermophysics 33 ( 1 ): 172 – 183 .
  • Erbay , H. A. , Erbay , S. , Dost , S. ( 1991 ). Thermally induced vibrations in a generalized thermoelastic solid with a cavity . Journal of Thermal Stresses 14 ( 2 ): 161 – 171 .
  • Green , A. E. , Lindsay , K. A. ( 1972 ). Thermoelasticity . Journal of Elasticity 2 ( 1 ): 1 – 7 .
  • Hetnarski , R. B. , Ignaczak , J. ( 1999 ). Generalized thermoelasticity . Journal of Thermal Stresses 22 ( 4 ): 451 – 476 .
  • Hosseini , S. M. , Abolbashari , M. H. ( 2012 ). Analytical solution for thermoelastic waves propagation analysis in thick hollow cylinder based on Green-Naghdi model of coupled thermoelasticity . Journal of Thermal Stresses 35 ( 4 ): 363 – 376 .
  • Lord , H. W. , Shulman , Y. ( 1967 ). A generalized dynamical theory of thermoelasticity . Journal of the Mechanics and Physics of Solids 15 ( 5 ): 299 – 309 .
  • Marin , M. , Lupu , M. ( 1998 ). On harmonic vibrations in thermoelasticity of micropolar bodies . JVC/Journal of Vibration and Control 4 ( 5 ): 507 – 518 .
  • Nayfeh , A. H. , Younis , M. I. ( 2004 ). Modeling and simulations of thermoelastic damping in microplates . Journal of Micromechanics and Microengineering 14 ( 12 ): 1711 – 1717 .
  • Othman , M. I. A. , Abbas , I. A. ( 2011 ). Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method . Meccanica 46 ( 2 ): 413 – 421 .
  • Othman , M. I. A. , Abbas , I. A. ( 2012 ). Generalized thermoelasticity of thermal-shock problem in a non-homogeneous isotropic hollow cylinder with energy dissipation . International Journal of Thermophysics 33 ( 5 ): 913 – 923 .
  • Qatu , M. S. , Leissa , A. W. (1993). Vibration of shallow shells with two adjacent edges clamped and the others free*. Journal of Structural Mechanics 21(3):285–301.
  • Rodrigues , J. , Roque , C. , Ferreira , A. J. ( 2013 ). An improved meshless method for the static and vibration analysis of plates . Mechanics Based Design of Structures and Machines 41 ( 1 ): 21 – 39 .
  • Sharma , J. N. , Sharma , N. ( 2011 ). Vibration analysis of homogeneous transradially isotropic generalized thermoelastic spheres . Journal of Vibration and Acoustics, Transactions of the ASME 133 ( 4 ): 041001 .
  • Sharma , J. N. , Singh , H. , Sharma , Y. D. ( 2011 ). Vibration analysis of a transversely isotropic hollow cylinder by using the matrix Frobenius method . Journal of Thermal Stresses 34 ( 9 ): 934 – 957 .
  • Sherief , H. H. , Ezzat , M. A. ( 1998 ). A problem in generalized magneto-thermoelasticity for an infinitely long annular cylinder . Journal of Engineering Mathematics 34 ( 1–4 ): 387 – 402 .
  • Wang , C. ( 2003 ). Vibration of a rigid body suspended by taut strings . Mechanics Based Design of Structures and Machines 31 ( 4 ): 563 – 570 .
  • Zenkour , A. M. , Abouelregal , A. E. ( 2014 ). State-space approach for an infinite medium with a spherical cavity based upon two-temperature generalized thermoelasticity theory and fractional heat conduction . Zeitschrift fur Angewandte Mathematik und Physik 65 ( 1 ): 149 – 164 .
  • Zenkour , A. , Mashat , D. , Abouelregal , A. ( 2012 ). Generalized thermodiffusion for an unbounded body with a spherical cavity subjected to periodic loading . Journal of Mechanical Science and Technology 26 ( 3 ): 749 – 757 .
  • Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lmbd.

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