Reflection and transmission of plane waves from fluid-piezothermoelastic solid interface

doi:10.1007/s10483-015-1892-9

Abstract

Abstract: The reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied. The expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically. The piezo-thermoelastic solid half-space is assumed to have 6mm type symmetry and assumed to be loaded with water. The effects of angle of the incidence, the frequency, the specific heat, the relaxation time, and the thermal conductivity on the reflected and transmitted energy ratios are studied numerically for a particular model of cadmium selenide (CdSe) and water. Some special cases are also studied.

Key words: transmission, thermal conductivity, piezo-thermoelastic, relaxation time, reflection

2010 MSC Number:

O414.1

A. K. VASHISHTH;H. SUKHIJA. Reflection and transmission of plane waves from fluid-piezothermoelastic solid interface. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 11-36.

TrendMD

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.amm.shu.edu.cn/EN/10.1007/s10483-015-1892-9

https://www.amm.shu.edu.cn/EN/Y2015/V36/I1/11

[1] Cady, W. G. Piezoelectricity, McGraw-Hill, New York (1946)
[2] Auld, B. A. Acoustic Field and Waves in Solids, Vol. II, Wiley InterScience, New York, 423 (1973)
[3] Auld, B. A. Acoustic Fields and Waves in Solids, Vol. I, Keieger Publishing Company, Malabar, Florida (1990)
[4] Ikeda, T. Fundamentals of Piezoelectricity, Oxford University Press, New York, 65-66 (1996)
[5] Arnau, A. Piezoelectric Transducers and Applications, 1st ed., Springer, New York (2004)
[6] Arnau, A. Piezoelectric Transducers and Applications, 2nd ed., Springer, New York (2008)
[7] Knott, C. G. Reflection and refraction of elastic waves with seismological applications. Philosophical Magazine, 48, 64-97 (1899)
[8] Crampin, S. and Taylor, D. B. The propagation of surface waves in anisotropic media. Geophysical Journal of the Royal Astronomical Society, 25, 71-87 (1971)
[9] Crampin, S. Distinctive particle motion of surface waves as a diagnostic of anisotropic layering. Geophysical Journal of the Royal Astronomical Society, 40, 177-186 (1975)
[10] Achenbach, J. D. Wave Propagation in Elastic Solids, North Holland Pub., Amsterdam (1973)
[11] Pal, A. K. and Chattopadhyay, A. The reflection phenomenon of plane waves at a free boundary in a pre-stressed elastic half-space. Journal of the Acoustical Society of America, 76(3), 924-925 (1984)
[12] Borejko, P. Reflection and transmission coefficients for three-dimensional plane waves in elastic media. Wave Motion, 24, 371-393 (1996)
[13] Ogden, R. W. and Sotirropoulos, D. The effect of pre-stress on the propagation and reflection of plane waves in incompressible elastic solids. IMA Journal of Applied Mathematics, 59, 95-121 (1997)
[14] Ogden, R. W. and Sotirropoulos, D. Reflection of plane wave from the boundary of a pre-stressed compressible elastic half-space. IMA Journal of Applied Mathematics, 61, 61-90 (1998)
[15] Chattopadhyay, A. and Rogerson, G. A.Wave reflection in slightly compressible, finitely deformed elastic media. Archive of Applied Mechanics, 71, 307-316 (2001)
[16] Chattopadhyay, A. Wave reflection in triclinic crystalline medium. Archive of Applied Mechanics, 76, 65-74 (2006)
[17] Deschamps, M. Reflection and refraction of the evanescent plane wave on plane interfaces. Journal of the Acoustical Society of America, 96, 2841-2848 (1991)
[18] Lord, H. W. and Shulman, Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15, 299-309 (1967)
[19] Green, A. E. and Lindsay, K. A. Thermoelasticity. Journal of Elasticity, 2, 1-7 (1972)
[20] Deresiewicz, H. Effect of boundaries on waves in a thermoelastic solid: reflection of plane wave from plane boundary. Journal of the Mechanics and Physics of Solids, 8, 164-172 (1960)
[21] Sinha, A. N. and Sinha, S. B. Reflection of thermoelastic waves at a solid half-space with thermal relaxation. Journal of Physics of the Earth, 22, 237-244 (1974)
[22] Singh, B. Reflection of plane sound wave from a micropolar generalized thermoelastic solid half-space. Journal of Sound and Vibration, 235, 685-696 (2000)
[23] Sinha, S. B. and Elsibai, K. A. Reflection and refraction of thermoelastic wave at an interface of two semi-infinite media with two thermal relaxation times. Journal of Thermal Stresses, 20, 129-146 (1997)
[24] Abd-Alla, A. N. and Al-Dawy, A. S. The reflection phenomenon of SV waves in a generalized thermoelastic medium. International Journal of Mathematics and Mathematical Sciences, 23, 529-546 (2000)
[25] Sharma, J. N., Kumar, V., and Chand, D. Reflection of generalized thermoelastic wave from the boundary of a half-space. Journal of Thermal Stresses, 26, 925-942 (2003)
[26] Deschamps, M. and Cheng, C. Liquid-thermoviscoelastic solids interface. Ultrasonics, 27, 308-313 (1989)
[27] Parton, V. Z. and Kudryavtsev, B. A. Electromagnetoelasticity, Piezoelectrics and Electrically Conductive Solids, Gorden and Breach, New York, 503 (1988)
[28] Noorbehesht, B. and Wade, G. Spatial frequency characteristics of opto-acoustic transducers. Acoustical Imaging (ed. Wang, K. Y.), Vol. 9, Plenum, New York, 139-154 (1980)
[29] Noorbehesht, B. and Wade, G. Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water. Journal of the Acoustical Society of America, 67(6), 1947-1953 (1980)
[30] Nayfeh, A. D. and Chien, H. T. The influence of piezoelectricity on free and reflected waves from fluid loaded anisotropic plates. Journal of the Acoustical Society of America, 91(3), 1250-1261 (1992)
[31] Nayfeh, A. D. and Chien, H. T. Wave propagation interaction with free and fluid loaded piezo-electric substrates. Journal of the Acoustical Society of America, 91(6), 3126-3135 (1992)
[32] Mindlin, R. D. On the equations of motion of piezoelectric crystals. Problem of Continuum 290 Mechanics (ed. Muskhelishvili, N. I.), 70th Birthday Volume, SIAM, Philadelphia, 282-290 (1961)
[33] Mindlin, R. D. Equations of high frequency vibrations of thermopiezoelectric crystal plates. International Journal of Solids and Structures, 10, 625-637 (1974)
[34] Nowacki, W. Some general theorems of thermopiezoelectricity. Journal of Thermal Stresses, 1, 171-182 (1978)
[35] Chandrasekharairh, D. S. A temperature rate dependent theory of thermoelasticity. Journal of Thermal Stresses, 7, 293-306 (1984)
[36] Sharma, J. N. and Pal, M. Propagation of Lamb waves in a transversely isotropic piezothermoe-lastic plate. Journal of Sound and Vibration, 270, 587-610 (2004)
[37] Sharma, J. N., Kumar, V., and Chand, D. Reflection of generalized thermoelastic waves from boundary of a half space. Journal of Thermal Stresses, 26, 925-942 (2003)
[38] Sharma, J. N., Walia, V., and Gupta, S. K. Effect of rotation and thermal relaxation on Rayleigh waves in piezothermoelastic half space. International Journal of Mechanical Sciences, 50(3), 433-444 (2008)
[39] Sharma, M. D. Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media. Acta Mechanica, 25, 307-318 (2010)
[40] Sharma, J. N., Walia, V., and Gupta, S. K. Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space. International Journal of Engineering Science, 46, 131-146 (2008)
[41] Mott, G. Reflection and refraction coefficients at a fluid-solid interface. Journal of the Acoustical Society of America, 50, 819-829 (1970)
[42] Singh, B. Plane waves in a thermally conducting viscous liquid. Sadhna, 29(1), 27-34 (2004)
[43] Vashishth, A. K. and Sharma, M. D. Reflection and refraction of acoustic waves at poroelastic ocean bed. Earth Planet Space, 61, 675-687 (2009)
[44] Scott, N. H. Energy and dissipation of inhomogeneous plane waves in thermoelasticity. Wave Motion, 23, 393-406 (1996)
[45] Kuang, Z. B. and Yuan, X. G. Reflection and transmission of waves in pyroelectric and piezoelectric materials. Journal of Sound and Vibration, 330, 1111-1120 (2011)
[46] Vashishth, A. K. and Gupta, V. Reflection and transmission of plane waves from a fluid-porous piezoelectric solid interface. Journal of the Acoustical Society of America, 129(6), 3690-3701 (2011)
[47] Krebes, E. S. The viscoelastic reflection/transmission problem: two special cases. Bulletin of the Seismological Society of America, 73(6), 1673-1683 (1983)
[48] Stoll, R. D. and Kan, T. K. Reflection of acoustic waves at a water-sediment interface. Journal of the Acoustical Society of America, 70, 149-156 (1981)
[49] Borcherdt, R. D., Glassmoyer, G., and Wennerberg, L. Influence of welded boundaries in anelastic media on energy flow, and characterestics of P, S-I and S-II waves: observational evidence for inhomogeneous body waves in low-loss solids. Journal of Geophysical Research, 91(B11), 11503-11518 (1986)
[50] Ankan, O., Telatar, E., and Atalar, A. Reflection coefficient null of acoustic waves at a liquid-anisotropic solid interface. Journal of the Acoustical Society of America, 85(1), 1-10 (1989)
[51] Mayer, G. W. Reflection and refraction of mechanical waves at solid liquid boundaries. Journal of Applied Physics, 34, 909-912 (1963)

Reflection and transmission of plane waves from fluid-piezothermoelastic solid interface

RichHTML

PDF

Knowledge

Cited

Abstract

Cite this article

share this article

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Xinbiao XIAO, Xinte WANG, Jian HAN, Yuanpeng HE. Comparative study on vibro-acoustic properties of sandwich shells containing functionally-graded porous materials in a thermal environment [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 947-964.
[2]	M. R. ZARASTVAND, E. ABDOLI, R. TALEBITOOTI. A lattice metamaterial-based sandwich cylindrical system for numerical simulation approach of vibroacoustic transmission considering triply periodic minimal surface [J]. Applied Mathematics and Mechanics (English Edition), 2025, 46(11): 2035-2054.
[3]	Chao WANG, Honggang ZHAO, Yang WANG, Jie ZHONG, Dianlong YU, Jihong WEN. Topology optimization of chiral metamaterials with application to underwater sound insulation [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1119-1138.
[4]	Yabin JING, Lifeng WANG, Yuqiang GAO. Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1107-1118.
[5]	M. SAFI, M. VAKILIFARD, M.J. MAHMOODI. Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 407-424.
[6]	Jinhui LIU, Yu XUE, Zhihong GAO, A. O. KRUSHYNSKA, Jinqiang LI. Actively tunable sandwich acoustic metamaterials with magnetorheological elastomers [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1875-1894.
[7]	Wenhao YUAN, Haitao LIAO, Ruxin GAO, Fenglian LI. Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 897-916.
[8]	Feiyang HE, Zhiyu SHI, Denghui QIAN, Y. K. LU, Yujia XIANG, Xuelei FENG. Flexural wave bandgap properties of phononic crystal beams with interval parameters [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(2): 173-188.
[9]	Wenzheng QUE, Xiaodong YANG, Wei ZHANG. Tunable low frequency band gaps and sound transmission loss of a lever-type metamaterial plate [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1145-1158.
[10]	Yongbin WANG, Huadong YONG, Youhe ZHOU. Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(5): 689-708.
[11]	Zhenni LI, Yize WANG, Yuesheng WANG. Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(2): 167-184.
[12]	P. SINGH, A. K. SINGH, A. CHATTOPADHYAY. Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1363-1378.
[13]	T. MUSHTAQ, A. RAUF, S. A. SHEHZAD, F. MUSTAFA, M. HANIF, Z. ABBAS. Numerical and statistical approach for Casson-Maxwell nanofluid flow with Cattaneo-Christov theory [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 1063-1076.
[14]	T. SAEED, I. A. ABBAS. Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 927-938.
[15]	K. LOTFY, A. K. KHAMIS, A. A. EL-BARY, M. H. AHMED. Thomson and rotation effects during photothermal excitation process in magnetic semiconductor medium using variable thermal conductivity [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(6): 909-926.