Engineering Transactions, 47, 3-4, pp. 299–319, 1999

On the Propagation of Generalized Thermoelastic Vibrations in Plates

K.L. Verma
Government Post-Graduate College Hamirpur

N. Hasebe
Nagoya Institute of Technology

The heat conduction equation in the context of generalized theories of thermoelasticity is used to study the propagation of plane harmonic waves in a thin, flat, infinite, homogeneous, thermoelastic isotropic plate of finite width. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained, and some limiting cases of the frequency equations are then discussed. The comparison of the results for the theories of generalized thermoelasicity have also been made. The results obtained have been verified numerically and are represented graphically for aluminum epoxy composite plate.
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J. IGNACZAK, Generalized thermoelasticity and its applications, [in:] R.B. Hetnarski [Ed.], Thermal Stresses III, Elsevier Science Publishers B.V., 1989.

S. KALISKI, Wave equations of thermoelasticity, Bull. Acad. Sci. Ser. Sci. Techn. 13, 253, 1965.

N. FOX, Generalized thermoelasticity, Int. J. Engg. Sci., 7, 437, 1969.

M.E. GUKTIN, A.C. PIPKI, A general theory of heat conduction, Arch. Mech. Anal., 31, 113, 1968.

J. MEIXNER, On linear theory of heat conduction, Arch. Rat. Mech. Anal., 39, 108, 1970.

B.A. BOLEY, High temperature structures and materials, Pergamon Press, Oxford, 1964.

H.W. LORD and Y. SHULMAN, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299, 1967.

C.C. ACKERMAN,, Second sound in solid helium, Phys. Rev. Lett., 16, 789, 1966.

A. NAYFEH, S.N. NASSER, Thermoelastic waves in a solid with thermal relaxations, Acta Mechanica, 12, 53, 1971.

S.G. MONDAL, On the propagation of a thermoelastic wave in a thin infinite plate immersed in an infinite liquid with thermal relaxations, Indian J. Pure Appl. Math., 14, 185, 1983.

D.S. CHANDRASEKHARAIAH, Thermoelasticity with second sound, A review, Appl, Mech. Rev., 39, 355–376, 1986.

A.E. GREEN and P.M. NAGDHI, A re-examination of the basic postulates of thermodynamics, Proc. Roy. Soc. London Ser A, 432, 171–194, 1991.

A.E. GREEN and P.M. NAGHDI, Thermoleasticity without energy dissipation, J. Elasticity, 31, 189–208, 1993.

D.S. CHANDRASEKHARAIAH, A uniqueness theorem in the theory of thermoelasticity without energy dissipation, J. Thermal Stresses, 19, 1996.

D.S. CHANDRASEKHARAIAH, One-dimensional wave propagation in the linear theory of thermoelasticity without energy dissipation, 3. Thermal Stresses, 19, 695–710, 1996.

A.E. GREEN and P.M. NAGHDI, On undamped heat waves in a elastic of solid, 15, 253–264, 1972.

HONGLI, R.S. DHALIWAL, Thermal shock problem in thermoelasticity without energy dissipation, Indian J. Pure App. Maths., 27, 85–101, 1996.

K.S. HARINATH, Surface point source in generalized thermoelastic half-space, Ind. J. Pure Appl. Math., 8, 1347–1351, 1975.

A. NAYFEH and S.N. NASSER, Transient thermoelastic waves in a half-space with thermal relaxations, J. Appl. Maths., Physics 23, 50–67, 1972.

P. CHADWICK, Progress in solid mechanics, [Eds. R. Hill and I.N. Sneddon], 1, North Holland Publishing Co., Amsterdam 1960.

F.J. LOCKETT, Effect of thermal properties of a solid on the velocity of Rayleigh waves, J. Mech. Phys. Solids 7, 71, 1985.

W.M. EWING, W.S. JARDETSKY, F. PRESS, Elastic waves in layered media, McGraw-Hill, New York 1957.

K.L. VERMA, Thermoelastic wave propagation problems in linear theory of thermoelasticity without energy dissipation, (comm.)

T.S. ONCU and T.B. MOODIE, Pade-extended Ray series expansions in generalized thermoelasticity, 3. Thermal Stresses, 14, 85–99, 1991.

T.S. ONCU, T.B. MOODIE, On the propagation of thermoelastic waves in temperature rate-depenent materials, J. Elasticity 29, 263–281, 1991.

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