Wave Propagation in a Layer of Binary Mixture of Elastic Solids

Document Type : Research Paper


Department of Mathematics, Kurukshetra University


This paper concentrates on the propagation of waves in a layer of binary mixture of elastic solids subjected to stress free boundaries. Secular equations for the layer corresponding to symmetric and antisymmetric wave modes are derived in completely separate terms. The amplitudes of displacement components and specific loss for both symmetric and antisymmetric modes are obtained. The effect of mixtures on phase velocity, attenuation coefficient, specific loss and amplitude ratios for symmetric and antisymmetric modes is depicted graphically. A particular case of interest is also deduced from the present investigation.


[1] Truesdell C., 1996, Mechanical basis of diffusion, Journal of Chemical Physics 37: 2336-2344.
[2] Truesdell C., Toupin R., 1960, Handbuch der Physik, 3/1: 469-472, 567- 568, 612-614, Springer.
[3] Bowen R.M., 1976, Theory of mixtures, in: Continuum Physics,edited byA.C.Eringen, 3, Academic Press, New York.
[4] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Applications, Journal of Applied Mathematics 17(2): 153-207.
[5] Atkin R.J., Craine R.E., 1976, Continuum theories of mixtures: Basic theory and historic development, Quarterly Journal of Mechanics and Applied Mathematics 29: 209-245.
[6] Bedford A., Drumheller D.S., 1983, Theory of immiscible and structured mixtures, International Journal of Engineering Science 21: 863-960.
[7] Samohyl I., 1987, Thermodynamics of Irreversible Processes in Fluid Mixtures, Teubner Verlag, Leibzig.
[8] Rajagopal K.R., Tao L., 1995, Mechanics of Mixtures, World Scientific, Singapore.
[9] Green A.E., Steel T.R., 1966, Constitutive equations for interacting continua, International Journal of Engineering Science 4: 483-500.
[10] Steel T.R., 1967, Applications of a theory of interacting continua, Quarterly Journal of Mechanics and Applied Mathematics 20: 57-72.
[11] Bedford A., Stern M., 1972, A multi-continuum theory for composite elastic materials, Acta Mechanica 14: 85-102.
[12] Bedford A., Stern M., 1972, Towards a diffusing continuum theory of composite elastic materials, ASME Transactions, Journal of Applied Mechanics 38: 8-14.
[13] Iesan D., Quintanilla R., 1994, Existance and continuous dependence results in the theory of interacting continua, Journal of Elasticity 36: 85-98.
[14] Tiersten H.F., Jahanmir M., 1977, A theory of composite modeled as interpenetrating solid continua, Archive for Rational Mechanics and Analysis 65: 153-192.
[15] Iesan D., 1994, On the theory of mixtures of elastic solids, Journal of Elasticity 35: 251-268.
[16] Iesan D., 1996, Existance theorems in the theory of mixtures, Journal of Elasticity 42: 145-163.
[17] Ciarletta M., 1998, On mixtures of nonsimple elastic solids, International Journal of Engineering Science 36: 655-668.
[18] Ciarletta M., Passarella F., 2001, On the spatial behavior in dynamics of elastic mixtures, European Journal of Mechanics A/Solids 20: 969-979.
[19] Iesan D., 2004, On the theory of viscoelastic mixtures, Journal of Thermal Stresses 27: 1125-1148.
[20] Quintanilla R., 2005, Existance and exponential decay in the linear theory of viscoelastic mixtures, European Journal of Mechanics A/Solids 24: 311-324.
[21] Iesan D., 2007, A theory of thermoviscoelastic composites modelled as interacting cosserat continua, Journal of Thermal Stresses 30: 1269-1289.
[22] Kolsky H., 1963, Stress Waves in Solids, Clarendon Press, Oxford Dover Press, New York.
[23] Graff K.F., 1975, Wave Motion in Elastic Solids, Clarendon Press, Oxford.