Surface Wave Propagation in a Generalized Thermoelastic Material with Voids

ABSTRACT

In the present paper, the propagation of surface wave in a generalized thermoelastic solid with voids is considered. The governing equations are solved to obtain the general solution in x-z plane. The appropriate boundary conditions at an interface between two dissimilar half-spaces are satisfied by appropriate particular solutions to obtain the frequency equation of the surface wave in the medium. Some special cases are also discussed.

In the present paper, the propagation of surface wave in a generalized thermoelastic solid with voids is considered. The governing equations are solved to obtain the general solution in x-z plane. The appropriate boundary conditions at an interface between two dissimilar half-spaces are satisfied by appropriate particular solutions to obtain the frequency equation of the surface wave in the medium. Some special cases are also discussed.

Cite this paper

nullB. Singh and R. Pal, "Surface Wave Propagation in a Generalized Thermoelastic Material with Voids,"*Applied Mathematics*, Vol. 2 No. 5, 2011, pp. 521-526. doi: 10.4236/am.2011.25068.

nullB. Singh and R. Pal, "Surface Wave Propagation in a Generalized Thermoelastic Material with Voids,"

References

[1] J. W. Nunziato and S. C. Cowin, “A Nonlinear Theory of Elastic Materials with Voids,” Archive for Rational Mechanics and Analysis, Vol. 72, No. 2, 1979, pp. 175-201.

[2] S. C. Cowin and J. W. Nunziato, “Linear Elastic Materials with Voids,” Journal of Elasticity, Vol. 13, No. 2, 1983, 125-147. doi:10.1007/BF00041230

[3] P. Puri and S. C. Cowin, “Plane Waves in Linear Elastic Materials with Voids,” Journal of Elasticity, Vol. 15, No. 2, 1985, pp. 167-183. doi:10.1007/BF00041991

[4] D. Iesan, “A Theory of Thermoelastic Materials with Voids,” Acta Mechanica, Vol. 60, No. 1-2, 1986, pp. 67- 89. doi:10.1007/BF01302942

[5] R. S. Dhaliwal and J. Wang, “A Heat-Flux Dependent Theory of Thermoelasticity with Voids,” Acta Mechanica, Vol. 110, No. 1-4, 1993, pp. 33-39.

[6] M. Ciarletta and A. Scalia, “On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids,” Journal of Applied Mathematics and Mechanics, Vol. 73, No. 2, 1993, pp. 67-75.

[7] M. Ciarletta and E. Scarpetta, “Some Results on TherMoelasticity for Dielectric Materials with Voids,” Journal of Applied Mathematics and Mechanics, Vol. 75, No. 9, 1995, pp. 707-714.

[8] M. Marin, “A Uniqueness Result for Body with Voids in Linear Thermoelasticity,” Rendiconti di Matematica, Vol. 17, No. 1, 1997, pp. 103-113.

[9] M. Marin, “On the Domain of Influence in Thermoelasticity of Bodies with Voids,” Archiv der Mathematik, Vol. 33, No. 4, 1997, pp. 301-308.

[10] S. Chirita and A. Scalia, “On the Spatial and Temporal Behavior in Linear Thermoelasticity of Materials with Voids,” Journal of Thermal Stresses, Vol. 24, No. 5, 2001, pp. 433-455.

[11] S. D. Cicco and M. Diaco, “A Theory of Thermoelastic Materials with Voids without Energy Dissipation,” Journal of Thermal Stresses, Vol. 25, No. 5, 2002, pp. 493- 503. doi:10.1080/01495730252890203

[12] M. Ciarletta, B. Straughan and V. Zampoli, “Thermo- poroacoustic Acceleration Waves in Elastic Materials with Voids without Energy Dissipation,” International Journal of Engineering Science, Vol. 45, No. 9, 2007, pp. 736-743. doi:10.1016/j.ijengsci.2007.05.001

[13] B. Singh, “Wave Propagation in a Generalized Thermoelastic Material with Voids,” Applied Mathematics and Computation, Vol. 189, No. 1, 2007, pp. 698-709. doi:10.1016/j.amc.2006.11.123

[14] M. Ciarletta, M. Svanadze and L. Buonanno, “Plane Waves and Vibrations in the Theory of Micropolar Thermoelasticity for Materials with Voids,” European Journal of Mechanics-A-Solids, Vol. 28, No. 4, 2009, pp. 897-903. doi:10.1016/j.euromechsol.2009.03.008

[15] M. Aoudai, “A Theory of Thermoelastic Diffusion Ma- terial with Voids,” Zeitschrift für Angewandte Mathe- matik und Physik, Vol. 61, No. 2, 2010, pp. 357-379. doi:10.1007/s00033-009-0016-0

[16] L. Rayleigh, “On Waves Propagating along the Plane Surface of an Elastic Solid,” Proceedings of the London Mathematical Society, Vol. 17, No. 1, 1885, pp. 4-11. doi:10.1112/plms/s1-17.1.4

[17] D. S. Chandrasekharaiah, “Effects of Surface Stresses and Voids on Rayleigh Waves in an Elastic Solid,” International Journal of Engineering Science, Vol. 25, No. 2, 1987, pp. 205-211.

[18] P. Chadwick and D. W. Windle, “Propagation of Rayleigh Waves along Isothermal and Insulated Boundaries,” Proceedings of the Royal Society of America, Vol. 280, No. 1380, 1964, pp. 47-71. doi:10.1098/rspa.1964.0130

[19] V. K. Agarwal, “On Surface Waves in Generalized Thermoelasticity,” Journal of Elasticity, Vol. 8, No. 2, 1978, pp. 171-177. doi:10.1007/BF00052480

[20] J. N. Sharma and H. Singh, “Thermoelastic Surface Waves in a Transversely Isotropic Half-Space with Thermal Relaxation,” Indian Journal of Pure and Applied Mathematics, Vol. 16, No. 10, 1985, pp. 1202-1219.

[21] A. P. Mayer, “Thermoelastic Attenuation of Surface Acoustic Waves,” International Journal of Engineering Science, Vol. 28, No. 10, 1990, pp. 1073-1082. doi:10.1016/0020-7225(90)90135-6

[22] F. V. Semerak, “The Effect of Thermal Relaxation on Rayleigh Surface Waves in a Thermoelastic Medium,” Journal of Mathematical Sciences, Vol. 88, No. 3, 1997, pp. 396-399.

[23] D. S. Chandrasekharaiah, “Thermoelastic Rayleigh Waves without Energy Dissipation,” Mechanics Research Communication, Vol. 24, No. 1, 1997, pp. 93-102. doi:10.1016/S0093-6413(96)00083-3

[24] J. N. Sharma, D. Singh and R. Kumar, “Generalized Thermoelastic Waves in Homogeneous Isotropic Plates,” Journal of the Acoustical Society of America, Vol. 108, No. 2, 2000, pp. 848-851. doi:10.1121/1.429619

[25] J. N. Sharma and D. Kaur, “Rayleigh Waves in Rotating Thermoelastic Solids with Voids” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 3, 2010, pp. 43-61.

[26] H. W. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5

[1] J. W. Nunziato and S. C. Cowin, “A Nonlinear Theory of Elastic Materials with Voids,” Archive for Rational Mechanics and Analysis, Vol. 72, No. 2, 1979, pp. 175-201.

[2] S. C. Cowin and J. W. Nunziato, “Linear Elastic Materials with Voids,” Journal of Elasticity, Vol. 13, No. 2, 1983, 125-147. doi:10.1007/BF00041230

[3] P. Puri and S. C. Cowin, “Plane Waves in Linear Elastic Materials with Voids,” Journal of Elasticity, Vol. 15, No. 2, 1985, pp. 167-183. doi:10.1007/BF00041991

[4] D. Iesan, “A Theory of Thermoelastic Materials with Voids,” Acta Mechanica, Vol. 60, No. 1-2, 1986, pp. 67- 89. doi:10.1007/BF01302942

[5] R. S. Dhaliwal and J. Wang, “A Heat-Flux Dependent Theory of Thermoelasticity with Voids,” Acta Mechanica, Vol. 110, No. 1-4, 1993, pp. 33-39.

[6] M. Ciarletta and A. Scalia, “On the Nonlinear Theory of Nonsimple Thermoelastic Materials with Voids,” Journal of Applied Mathematics and Mechanics, Vol. 73, No. 2, 1993, pp. 67-75.

[7] M. Ciarletta and E. Scarpetta, “Some Results on TherMoelasticity for Dielectric Materials with Voids,” Journal of Applied Mathematics and Mechanics, Vol. 75, No. 9, 1995, pp. 707-714.

[8] M. Marin, “A Uniqueness Result for Body with Voids in Linear Thermoelasticity,” Rendiconti di Matematica, Vol. 17, No. 1, 1997, pp. 103-113.

[9] M. Marin, “On the Domain of Influence in Thermoelasticity of Bodies with Voids,” Archiv der Mathematik, Vol. 33, No. 4, 1997, pp. 301-308.

[10] S. Chirita and A. Scalia, “On the Spatial and Temporal Behavior in Linear Thermoelasticity of Materials with Voids,” Journal of Thermal Stresses, Vol. 24, No. 5, 2001, pp. 433-455.

[11] S. D. Cicco and M. Diaco, “A Theory of Thermoelastic Materials with Voids without Energy Dissipation,” Journal of Thermal Stresses, Vol. 25, No. 5, 2002, pp. 493- 503. doi:10.1080/01495730252890203

[12] M. Ciarletta, B. Straughan and V. Zampoli, “Thermo- poroacoustic Acceleration Waves in Elastic Materials with Voids without Energy Dissipation,” International Journal of Engineering Science, Vol. 45, No. 9, 2007, pp. 736-743. doi:10.1016/j.ijengsci.2007.05.001

[13] B. Singh, “Wave Propagation in a Generalized Thermoelastic Material with Voids,” Applied Mathematics and Computation, Vol. 189, No. 1, 2007, pp. 698-709. doi:10.1016/j.amc.2006.11.123

[14] M. Ciarletta, M. Svanadze and L. Buonanno, “Plane Waves and Vibrations in the Theory of Micropolar Thermoelasticity for Materials with Voids,” European Journal of Mechanics-A-Solids, Vol. 28, No. 4, 2009, pp. 897-903. doi:10.1016/j.euromechsol.2009.03.008

[15] M. Aoudai, “A Theory of Thermoelastic Diffusion Ma- terial with Voids,” Zeitschrift für Angewandte Mathe- matik und Physik, Vol. 61, No. 2, 2010, pp. 357-379. doi:10.1007/s00033-009-0016-0

[16] L. Rayleigh, “On Waves Propagating along the Plane Surface of an Elastic Solid,” Proceedings of the London Mathematical Society, Vol. 17, No. 1, 1885, pp. 4-11. doi:10.1112/plms/s1-17.1.4

[17] D. S. Chandrasekharaiah, “Effects of Surface Stresses and Voids on Rayleigh Waves in an Elastic Solid,” International Journal of Engineering Science, Vol. 25, No. 2, 1987, pp. 205-211.

[18] P. Chadwick and D. W. Windle, “Propagation of Rayleigh Waves along Isothermal and Insulated Boundaries,” Proceedings of the Royal Society of America, Vol. 280, No. 1380, 1964, pp. 47-71. doi:10.1098/rspa.1964.0130

[19] V. K. Agarwal, “On Surface Waves in Generalized Thermoelasticity,” Journal of Elasticity, Vol. 8, No. 2, 1978, pp. 171-177. doi:10.1007/BF00052480

[20] J. N. Sharma and H. Singh, “Thermoelastic Surface Waves in a Transversely Isotropic Half-Space with Thermal Relaxation,” Indian Journal of Pure and Applied Mathematics, Vol. 16, No. 10, 1985, pp. 1202-1219.

[21] A. P. Mayer, “Thermoelastic Attenuation of Surface Acoustic Waves,” International Journal of Engineering Science, Vol. 28, No. 10, 1990, pp. 1073-1082. doi:10.1016/0020-7225(90)90135-6

[22] F. V. Semerak, “The Effect of Thermal Relaxation on Rayleigh Surface Waves in a Thermoelastic Medium,” Journal of Mathematical Sciences, Vol. 88, No. 3, 1997, pp. 396-399.

[23] D. S. Chandrasekharaiah, “Thermoelastic Rayleigh Waves without Energy Dissipation,” Mechanics Research Communication, Vol. 24, No. 1, 1997, pp. 93-102. doi:10.1016/S0093-6413(96)00083-3

[24] J. N. Sharma, D. Singh and R. Kumar, “Generalized Thermoelastic Waves in Homogeneous Isotropic Plates,” Journal of the Acoustical Society of America, Vol. 108, No. 2, 2000, pp. 848-851. doi:10.1121/1.429619

[25] J. N. Sharma and D. Kaur, “Rayleigh Waves in Rotating Thermoelastic Solids with Voids” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 3, 2010, pp. 43-61.

[26] H. W. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, 1967, pp. 299-309. doi:10.1016/0022-5096(67)90024-5