Thermoelastic Waves in Anisotropic Platesusing Normal Mode Expansion Method with Thermal Relaxation Time
Analysis for the generalized thermoelastic Lamb
waves, which propagates in anisotropic thin plates in generalized
thermoelasticity, is presented employing normal mode expansion
method. The displacement and temperature fields are expressed by a
summation of the symmetric and antisymmetric thermoelastic modes
in the surface thermal stresses and thermal gradient free orthotropic
plate, therefore the theory is particularly appropriate for waveform
analyses of Lamb waves in thin anisotropic plates. The transient
waveforms excited by the thermoelastic expansion are analyzed for
an orthotropic thin plate. The obtained results show that the theory
provides a quantitative analysis to characterize anisotropic
thermoelastic stiffness properties of plates by wave detection. Finally
numerical calculations have been presented for a NaF crystal, and the
dispersion curves for the lowest modes of the symmetric and
antisymmetric vibrations are represented graphically at different
values of thermal relaxation time. However, the methods can be used
for other materials as well
[1] J. D. Achenbach, "Wave Propagation in Elastic Solids. North-Holland,
Amsterdam 1973.
[2] W. Nowacki, Dynamic Problems of Thermoelasticity. Noordho.,
Leyden, The Netherlands 1975.
[3] W. Nowacki, Thermoelasticity. 2nd edition. Pergamon Press, Oxford
1986.
[4] H. W. Lord, Y. Shulman, A generalized dynamical theory of
thermoelasticity. Journal of Mechanics and physics of Solids, 15, pp.
299-309, 1967.
[5] A.E. Green., K.A. Lindsay, Thermoelasticity, Journal of Elasticity 2, pp.
1-7, 1972.
[6] D. K. Banerjee, Y. K. Pao, Thermoelastic waves in anisotropy solids, J.
Acoust. Soc. Am. 56, pp. 1444-1453, 1974.
[7] R.S. Dhaliwal, H. H. Sherief, Generalized thermoelasticity for
anisotropic media, Quarterly Applied Mathematics 38, pp. 1-8, 1980.
[8] D.S Chandrasekharaiah, Thermoelasticity with second sound: a review.
Applied Mechanics Review 39 pp. 355-376, 1986.
[9] D.S Chandrasekharaiah, Hyperbolic thermoelasticity: a review of recent
literature. Applied Mechanics Review 51, pp.705-729, 1998.
[10] P. Chadwick, Progress in Solid Mechanics, Eds R. Hill and I.N.
Sneddon 1 North Holland Publishing Co., Amsterdam 1960.
[11] K. L Verma, On the thermo-mechanical coupling and dispersion of
thermoelastic waves with thermal relaxations. International Journal
applied and Mathematics and Statistics, 3, S05, pp. 34-50, 2005.
[12] K. L Verma, Thermoelastic vibrations of transversely isotropic plate
with thermal relaxations. International Journal of Solids and Structures,
38, pp. 8529-8546, 2001.
[13] K. L. Verma, N. Hasebe, On The Flexural and extensional thermoelastic
waves in orthotropic with thermal relaxation times. Journal of Applied
Mathematics, 1, 69-83, 2004.
[14] K. L. Verma, N. Hasebe, Wave propagation in plates of general
anisotropic media in generalized thermoelasticity, International Journal
of Engineering Science, 39(15), 1739-1763, (2001.
[15] K. L. Verma, N. Hasebe, Wave propagation in transversely isotropic
plates in generalized thermoelasticity. Arch. Appl. Mech. 72(6-7), pp.
470-482, 2002.
[16] C. V. Massalas, Thermoelastic waves in a thin plate. Acta Mechanica,
65, pp. 51-62, 1986.
[17] A.H. Nayfeh, S. N Nasser,. Thermoelastic waves in a solid with thermal
relaxations, Acta Mechanica, 12, pp.53-69, 1971.
[18] C. V. Massalas, V. K. Kalpakidis, Thermoelastic waves in a thin plate
with mixed boundary conditions and thermal relaxation. Ingenieur-
Archiv. 57, pp. 401-412, 1987.
[19] J. C. Cheng, S.Y. Zhang, Rev Prog., Quant. Non-Destr. Eval. 15, 253,
1996.
[20] J. C. Cheng, Y. Berthelot,. J. Phys. D 29, 1857, 1996.
[21] J. C. Cheng, S.Y. Zhang,. Normal mode expansion method for lasergenerated
ultrasonic lamb waves in orthotropic thin plates. Appl. Phys. B
70 pp. 57-63, 2000.
[22] C. Eringen, E. S. Suhubi, Elastodynamics (Academic Press, New York)
Vol. 2, 8, 1975.
[1] J. D. Achenbach, "Wave Propagation in Elastic Solids. North-Holland,
Amsterdam 1973.
[2] W. Nowacki, Dynamic Problems of Thermoelasticity. Noordho.,
Leyden, The Netherlands 1975.
[3] W. Nowacki, Thermoelasticity. 2nd edition. Pergamon Press, Oxford
1986.
[4] H. W. Lord, Y. Shulman, A generalized dynamical theory of
thermoelasticity. Journal of Mechanics and physics of Solids, 15, pp.
299-309, 1967.
[5] A.E. Green., K.A. Lindsay, Thermoelasticity, Journal of Elasticity 2, pp.
1-7, 1972.
[6] D. K. Banerjee, Y. K. Pao, Thermoelastic waves in anisotropy solids, J.
Acoust. Soc. Am. 56, pp. 1444-1453, 1974.
[7] R.S. Dhaliwal, H. H. Sherief, Generalized thermoelasticity for
anisotropic media, Quarterly Applied Mathematics 38, pp. 1-8, 1980.
[8] D.S Chandrasekharaiah, Thermoelasticity with second sound: a review.
Applied Mechanics Review 39 pp. 355-376, 1986.
[9] D.S Chandrasekharaiah, Hyperbolic thermoelasticity: a review of recent
literature. Applied Mechanics Review 51, pp.705-729, 1998.
[10] P. Chadwick, Progress in Solid Mechanics, Eds R. Hill and I.N.
Sneddon 1 North Holland Publishing Co., Amsterdam 1960.
[11] K. L Verma, On the thermo-mechanical coupling and dispersion of
thermoelastic waves with thermal relaxations. International Journal
applied and Mathematics and Statistics, 3, S05, pp. 34-50, 2005.
[12] K. L Verma, Thermoelastic vibrations of transversely isotropic plate
with thermal relaxations. International Journal of Solids and Structures,
38, pp. 8529-8546, 2001.
[13] K. L. Verma, N. Hasebe, On The Flexural and extensional thermoelastic
waves in orthotropic with thermal relaxation times. Journal of Applied
Mathematics, 1, 69-83, 2004.
[14] K. L. Verma, N. Hasebe, Wave propagation in plates of general
anisotropic media in generalized thermoelasticity, International Journal
of Engineering Science, 39(15), 1739-1763, (2001.
[15] K. L. Verma, N. Hasebe, Wave propagation in transversely isotropic
plates in generalized thermoelasticity. Arch. Appl. Mech. 72(6-7), pp.
470-482, 2002.
[16] C. V. Massalas, Thermoelastic waves in a thin plate. Acta Mechanica,
65, pp. 51-62, 1986.
[17] A.H. Nayfeh, S. N Nasser,. Thermoelastic waves in a solid with thermal
relaxations, Acta Mechanica, 12, pp.53-69, 1971.
[18] C. V. Massalas, V. K. Kalpakidis, Thermoelastic waves in a thin plate
with mixed boundary conditions and thermal relaxation. Ingenieur-
Archiv. 57, pp. 401-412, 1987.
[19] J. C. Cheng, S.Y. Zhang, Rev Prog., Quant. Non-Destr. Eval. 15, 253,
1996.
[20] J. C. Cheng, Y. Berthelot,. J. Phys. D 29, 1857, 1996.
[21] J. C. Cheng, S.Y. Zhang,. Normal mode expansion method for lasergenerated
ultrasonic lamb waves in orthotropic thin plates. Appl. Phys. B
70 pp. 57-63, 2000.
[22] C. Eringen, E. S. Suhubi, Elastodynamics (Academic Press, New York)
Vol. 2, 8, 1975.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:52343", author = "K.L. Verma", title = "Thermoelastic Waves in Anisotropic Platesusing Normal Mode Expansion Method with Thermal Relaxation Time", abstract = "Analysis for the generalized thermoelastic Lamb
waves, which propagates in anisotropic thin plates in generalized
thermoelasticity, is presented employing normal mode expansion
method. The displacement and temperature fields are expressed by a
summation of the symmetric and antisymmetric thermoelastic modes
in the surface thermal stresses and thermal gradient free orthotropic
plate, therefore the theory is particularly appropriate for waveform
analyses of Lamb waves in thin anisotropic plates. The transient
waveforms excited by the thermoelastic expansion are analyzed for
an orthotropic thin plate. The obtained results show that the theory
provides a quantitative analysis to characterize anisotropic
thermoelastic stiffness properties of plates by wave detection. Finally
numerical calculations have been presented for a NaF crystal, and the
dispersion curves for the lowest modes of the symmetric and
antisymmetric vibrations are represented graphically at different
values of thermal relaxation time. However, the methods can be used
for other materials as well", keywords = "Anisotropic, dispersion, frequency, normal,thermoelasticity, wave modes.", volume = "2", number = "1", pages = "8-8", }