Crested Waves in Thermoelastic Plates Immersed in Liquid

Abstract

The propagation of circularly crested generalized thermoelastic waves in a homogeneous isotropic, thermally conducting plate, bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides, is investigated in the context of conventional coupled thermoelasticity, and Lord-Shulman and Green-Lindsay theories of thermoelasticity. We derive secular equations for a circular homogeneous isotropic plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms. Results for the uncoupled theory of thermoelasticity have been obtained as a particular case from the present one. Special cases, such as Lam6 modes, short wavelength waves, and thin plate waves of the secular equation, are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for aluminum epoxy composite material bordered with water. The dispersion curves for symmetric and antisymmetric wave modes and amplitudes of displacement and temperature change in the case of fundamental symmetric (S_O) and skew symmetric (A_O) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.

Keywords

Crested waves generalized isotropic inviscid liquid Lamb waves

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References

Atkin, R. J. and Chadwick, P. , 1981, "Surface waves in heat conduction elastic body" Journal of Thermal Stresses 4, 509-522 (correction and extension of Chadwick and Windle, 1964).,

Banerjee, D. K. and Pao, Y. H. , 1974, "Thermoelastic waves in anisotropic solids," Journal of the Acoustical Society America 56, 1444-1453 .

Chadwick, P. , 1979, "Basic properties of plane harmonic waves in a prestressed heat conducting elastic material , Journal of Thermal Stresses 2, 193-214 .

Chadwick, P. and Windle, D. W. , 1964, "Propagation of Rayleigh waves along isothermal and insulated boundaries," Proceedings of the Royal Society of America 280, 47-54 .

Chandrasekharaiah, D. S. , 1986, "Thermoelasticity with second sound-a review," Applied Mechanics Review 39, 355-376 .

Dhaliwal, R. S. and Sherief, H. H. , 1980, "Generalized thermoelasticity for anisotropic media," Quarterly Applied Mathematics 38, 1-8 .

Graff, K. F. , 1991, Wave Motion in Elastic Solids, Dover, New York .

Green, A. E. and Lindsay, K. A. , 1972, "Thermoelasticity," Journal of Elasticity 2, 1-7 .

Kozlov, V. , 1972, "Thermoelastic vibrations of rectangular plates," Prikladnaya Mekhanika i Tekhnicheskaya Fizika 8, 123-127 .

10.

Kumar, A. B. , 1989, 'Thermoelastic waves from suddenly punched hole in stretched plate," Indian Journal of Pure and Applied Mathematics 20, 181-188 .

11.

Kurtze, G. and Bolt, R. H. , 1959, "On the interaction between plate bending wave and radiation load," Acoustica 9, 238-242 .

12.

Lord, H. W. and Shulman, Y , 1967, "The generalized dynamical theory of thermoelasticity," Journal of the Mechanics and Physics of Solids 15, 299-309 .

13.

Massalas, C. , Dalamangas, A. , and Leonditsis, A. , 1983, Symmetric non-linear response of a circular plate due to heat flux at z = h/2 Review of Romanian Science, Technology and Mechanical Applications 28,x 643-650 .

14.

Noda, N. , Furukwa, T. , and Ashida, F. , 1989, "Generalized thermoelasticity in an infinite solid with a hole," Journal of Thermal Stresses, 12, 385-403 .

15.

Schoch, V. A. , 1952, "Der schalldurchgang durch platten (Sound transmission in plates)," Acoustica 2, 1-17 .

16.

Scholte, J. G. , 1949, "On true and pseudo Rayleigh waves," Proceedings of K. Ned. Akad. Wet. Series 52, 652-653 .

17.

Sharma, J. N. , 2001, "On the propagation of thermoelastic waves in homogeneous isotropic plates," Indian Journal of Pure and Applied Mathematics 3, 1329-1341 .

18.

Sharma, J. N. and Pathania, V. , 2003, "Generalized thermoelastic Lamb waves in a plate bordered with layers of inviscid liquid," Journal of Sound and Vibration 268, 897-916 .

19.

Sharma, J. N. and Singh, D. , 2002, "Circular crested thermoelastic waves in homogeneous isotropic plates," Journal of Thermal Stresses 25, 1179-1193 .

20.

Sharma, J. N. , Singh, D. , and Kumar, R. , 2000, "Generalized thermoelastic waves in homogeneous isotropic plates," Journal of the Acoustical Society of America 108, 848-851 .

21.

Sharma, J. N. , Sharma, P. K. , and Sharma, R. L. , 2004, "Behavior of thermoelastic thick plate under lateral loads," Journal of Thermal Stresses 27, 171-191 .

22.

Watkins, R. D. , Cooper, W. H. B. , Gillespie, A. B. , and Pike, R. B. , 1982, "The attenuation of Lamb waves in the presence of a liquid," Ultrasonics 20, 257-264 .

23.

Wu, J. and Zhu, Z. , 1992, 'The propagation of Lamb waves in a plate bordered with layers of a liquid," Journal of the Acoustical Society of America 91, 861-867 .

24.

Zhu, Z. and Wu, J. , 1995, "The propagation of Lamb waves in a plate bordered with a viscous liquid," Journal of the Acoustical Society of America 98, 1057-1067 .