Wave Propagation at the Boundary Surface of Elastic Layer Overlaying a Thermoelastic Without Energy Dissipation Half-space
Subject Areas : Engineering
R Kumar
1
(Department of Mathematics, Kurukshetra University)
V Chawla
2
(Department of Mathematics, Kurukshetra University)
Keywords: Stiffness, Amplitudes, Thermoelasticity without energy dissipation,
Abstract :
The present investigation is to study the surface wave propagation at imperfect boundary between an isotropic thermoelastic without energy dissipation half-space and an isotropic elastic layer of finite thickness. The penetration depth of longitudinal, transverse, and thermal waves has been obtained. The secular equation for surface waves in compact form is derived after developing the mathematical model. The components of temperature distribution, normal and tangential stress are computed at the interface and presented graphically. The effect of stiffness is shown on the resulting amplitudes and the effect of thermal is shown on the penetration depth of various waves. A particular case of interest is also deduced. Some special cases of interest are also deduced from the present investigation.
[1] Benveniste Y., 1984, The effective mechanical behavior of composite materials with imperfect contact between the constituents, Mechanics of Materials 4: 197-208.
[2] Achenbaeh J.D., Zhu H., 1989, Effect of interfacial zone on mechanical behaviour and failure of reinforced composites, Journal of the Mechanics and Physics of Solids 37: 381-393.
[3] Hashin Z., 1990, Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials 8: 333-348.
[4] Hashin Z., 1991, The spherical inclusion with imperfect interface, ASME Journal of Applied Mechanics 58:444-449.
[5] Zhong Z., Meguid S. A., 1996, On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface, ASME Journal of Applied Mechanics 63: 877-883.
[6] Pan E., 2003, Three-dimensional Green’s function in anisotropic elastic bimaterials with imperfect interfaces, ASME Journal of Applied Mechanics 70: 180-190.
[7] Yu H.Y., 1998, A new dislocation-like model for imperfect interfaces and their effect on Lord transfer composites, Composite Part A: Applied Science and Manufacturing 29(9-10): 1057-1062.
[8] Yu H.Y., Wei Y.N., Chiang F.P., 2002, Lord transfer at imperfect interfaces dislocation-like model, International Journal of Engineering Science 40: 1647-1662.
[9] Benveniste Y., 1999, On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity, Journal of Applied Physics 86: 1273-1279.
[10] Joseph D.D., Preziosi L., 1989, Heat waves, Reviews of Modern Physics 61: 41-73.
[11] Dreyer W., Struchtrup H., 1993, Heat pulse experiments revisited, Continuum Mechanics and Thermodynamics 5(1): 3-50.
[12] Caviglia G., Morro A., Straughan B., 1992, Thermoelasticity at cryogenic temperatures, International Journal of Non-linear Mechanics 27: 251-261.
[13] Chandrasekharaiah D.S., 1986, Thermoelasticity with second sound: A review, Applied Mechanics Review 39: 355-376.
[14] Chandrasekharaiah D.S., 1998, Hyperbolic thermoelasticity: A review of recent literature, Applied Mechanics Review 51: 705-729.
[15] Muller I., Ruggeri T., 1998, Rational and extended thermodynamics, Springer-Verlag, New York.
[16] Hetnarski R.B., Ignazack J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-470.
[17] Green A.E., Naghdi P.M., 1995, A unified procedure for construction of theories of deformable media. I. Classical continuum physics, II. Generalized continua, III. Mixtures of interacting continua, Proceedings of Royal Society London A 448: 335-356, 357-377, 379-388.
[18] Green A.E., Naghdi P.M., 1991, A reexamination of the basic posulales of thermomechanics, Proceedings of Royal Society London A 432: 171-194.
[19] Green A.E., Naghdi P.M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15: 253-264.
[20] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.
[21] Bullen K.E., 1963, An introduction of the theory of seismology, Cambridge University Press, Cambridge.
[22] Scott N.H., 1996, Energy and dissipation of inhomogeneous plane waves in thermoelasticity, Wave Motion 23: 393-406.
[23] Ciarletta M., 1999, Atheory of micropolar thermoelasticity without energy dissipation, Journal of Thermal Stresses 22: 581-594.
[24] Kalpakides V.K., Maugin G.A., 2004, Canonical formulation and conservation laws of thermoelasticity without energy dissipation, Reports of Mathematical Physics 23: 371-391.
[25] Othman M. I.A., Song Y., 2007, Reflection of plane waves from an elastic solid half-space under hydrostatic intial stress without energy dissipation, International Journal of Solids and Structures 44: 5651-5664.
[26] Chirit S., Ciarletta M., 2010, Spatial behavior for some non-standard problems in linear thermoelasticity without energy dissipation,Journal of Mathematical Analysis and Applications 367: 58-68.
[27] Jiangong Y., Zhang X.., Xue T., 2010, Generalized thermoelastic waves in a functionally graded plates without energy dissipation, Composites Structures 93: 32-39.
[28] Jiangong Y., Bin W., Cunfu H., 2010, Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation, Ultrasonics 50: 416-423.
[29] Youssef H.M., 2011, Theory of two temperature thermoelasticity without energy dissipation, Journal of Thermal Stresses 34: 138-146.
[30] Jiangong Y., Bin W., Cunfu H., 2011, Guided thermoelastic wave propagation in layered plates without energy dissipation, Acta Mechanica Solida Sinica 24: 135-143.
[31] Aki K., Richards P.G., 1980, Quantitative Seismology Theory and Methods, Volume 1, Freeman, New York.
[32] Dhaliwal R.S., Singh A., 1980, Dynamical Coupled Thermoelasticity, Hindustan Publishing Corporation, Delhi, India.