DOI QR코드

DOI QR Code

Vibration analysis of wave motion in micropolar thermoviscoelastic plate

  • Kumar, Rajneesh (Department of Mathematics, Kurukshetra University) ;
  • Partap, Geeta (Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology)
  • 투고 : 2010.01.25
  • 심사 : 2010.06.24
  • 발행 : 2011.09.25

초록

The aim of the present article is to study the micropolar thermoelastic interactions in an infinite Kelvin-Voigt type viscoelastic thermally conducting plate. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's and Green and Lindsay's are employed by assuming the mechanical behaviour as dynamic to study the problem. The model has been simplified by using Helmholtz decomposition technique and the resulting equations have been solved by using variable separable method to obtain the secular equations in isolated mathematical conditions for homogeneous isotropic micropolar thermo-viscoelastic plate for symmetric and skew-symmetric wave modes. The dispersion curves, attenuation coefficients, amplitudes of stresses and temperature distribution for symmetric and skew-symmetric modes are computed numerically and presented graphically for a magnesium crystal.

키워드

참고문헌

  1. Baksi, A., Roy, B.K. and Bera, R.K. (2008), "Study of two dimensional visco-elastic problems in generalized thermoelastic medium with heat source", Struct. Eng. Mech., 29, 673-687. https://doi.org/10.12989/sem.2008.29.6.673
  2. Biswas, P.K., Sengupta P.R. and Debnath, L. (1996), "Axisymmetric Lamb's problem in a semi- infinite micropolar viscoelastic medium", Int. Math. Math. Sci., 19, 815-820. https://doi.org/10.1155/S0161171296001135
  3. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.
  4. Eringen, A.C. (1966), "Linear theory of micropolar elasticity", J. Math. Mech., 15, 909-923.
  5. Eringen, A.C. (1967), "Linear theory of micropolar viscoelasticity", Int. J. Eng. Sci., 5, 191-204. https://doi.org/10.1016/0020-7225(67)90004-3
  6. Eringen, A.C. (1984), "Plane waves in non-local micropolar elasticity", Int. J. Eng. Sci., 22, 1113-1121. https://doi.org/10.1016/0020-7225(84)90112-5
  7. Eringen, A.C. (1999), Microcontinuum Field Theories, I. Foundations and Solids, Springer-Verlag, New York.
  8. EI-Karamany Ahmed, S. (2003), "Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity", Int. J. Eng. Sci., 40, 2097-2117.
  9. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elasticity, 2, 1-7. https://doi.org/10.1007/BF00045689
  10. Kozar, I. and Ozbolt, J. (2010), "Some aspects of load-rate sensitivity in visco-elastic microplane material model", Comput. Concrete, 7, 317-329. https://doi.org/10.12989/cac.2010.7.4.317
  11. Kumar, R. (2000), "Wave propagation in a micropolar viscoelastic generalized thermoelastic solid", Int. J. Eng. Sci., 38, 1377-1395. https://doi.org/10.1016/S0020-7225(99)00057-9
  12. Kumar, R. and Partap, G. (2008), "Analysis of free vibrations for Rayleigh-Lamb waves in a micropolar viscoelastic plate", Int. J. Appl. Mech. Eng., 13, 383-397.
  13. Kumar, R. and Sharma, N. (2008), "Propagation of waves in micropolar viscoelastic generalized themoelastic solids having interficial imperfections", Theor. Appl. Fract. Mec., 50, 226-234. https://doi.org/10.1016/j.tafmec.2008.07.010
  14. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  15. McCarthy, M.F. and Eringen, A.C. (1969), "Micropolar viscoelastic waves", Int. J. Eng. Sci., 7, 447-458. https://doi.org/10.1016/0020-7225(69)90032-9
  16. Nowacki, W. (1966), "Couple stresses in the theory of thermoelasticity III", Bull. Acad. Polon. Sci. Ser. Sci. Tech., 14, 801-809.
  17. Sharma, J.N. (2005), "Some considerations on the Rayleigh-Lamb wave propagation in visco-thermoelastic plate", J. Vib. Control, 11, 1311-1335. https://doi.org/10.1177/1077546305058267
  18. Sharma, J.N. and Othman, Mohamad I.A. (2007), "Effect of rotation on generalized thermo-viscoelastic Rayleigh-Lamb waves", Int. J. Solids Struct., 44, 4243-4255. https://doi.org/10.1016/j.ijsolstr.2006.11.016
  19. Sharma, J.N., Chand, R. and Othman, Mohamad I.A. (2009), "On the propagation of Lamb waves in viscothermoelastic plates under fluid loading", Int. J. Eng. Sci., 47, 391-404. https://doi.org/10.1016/j.ijengsci.2008.10.008
  20. Simonetti, F. (2004), "Lamb wave propagation in elastic plates coated with viscoelastic materials", J. Acoust. Soc. Am., 115, 2041-2053. https://doi.org/10.1121/1.1695011

피인용 문헌

  1. Edge wave propagation in an Electro-Magneto-Thermoelastic homogeneous plate subjected to stress vol.53, pp.6, 2015, https://doi.org/10.12989/sem.2015.53.6.1201
  2. Analysis of stress, magnetic field and temperature on coupled gravity-Rayleigh waves in layered water-soil model vol.9, pp.1, 2015, https://doi.org/10.12989/eas.2015.9.1.111
  3. Thermoviscoelastic Behavior in a Circular HSLA Steel Plate vol.36, pp.10, 2013, https://doi.org/10.1080/01495739.2013.818895
  4. Dispersion of torsional surface wave in an intermediate vertical prestressed inhomogeneous layer lying between heterogeneous half spaces vol.23, pp.19, 2017, https://doi.org/10.1177/1077546316628706
  5. A magneto-thermo-viscoelastic problem with fractional order strain under GN-II model vol.63, pp.1, 2017, https://doi.org/10.12989/sem.2017.63.1.089
  6. Thermoviscoelastic orthotropic solid cylinder with variable thermal conductivity subjected to temperature pulse heating vol.13, pp.2, 2011, https://doi.org/10.12989/eas.2017.13.2.201