Analysis of Wave Motion in a Micropolar Transversely Isotropic Medium
الموضوعات :
R.R Gupta
1
(Department of Mathematics, Kurukshetra University, Kurukshetra)
R Kumar
2
(Department of Mathematics, Kurukshetra University, Kurukshetra)
الکلمات المفتاحية: Amplitude ratios, Micropolar, Transversely isotropic,
ملخص المقالة :
The present investigation deals with the propagation of waves in a micropolar transversely isotropic layer. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation were also obtained. Finally, the numerical solution was carried out for aluminium epoxy material and the dispersion curves. Amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented to evince the effect of anisotropy. Some particular cases are also deduced.
[1] Suhubi E.S., Eringen A.C., 1964, Non-linear theory of simple microelastic solids II, International Journal of Engineering Science 2: 389-404.
[2] Eringen A.C., 1999, Microcontinuum Field Theories I: Foundations and Solids, Springer-Verlag, New York.
[3] Mindlin R.D., 1964, Microstructure in linear elasticity, Archive for Rational Mechanics and Analysis, 16: 51-78.
[4] Eringen A.C., 1966, Linear theory of micropolar elasticity, Journal of Mathematical Mechanics 15(6): 909-923.
[5] Abubakar, I., 1962, Free vibrations of a transversely isotropic plate, Quarterly Journal of Mechanics and Applied XV, Pt. I: 129-136.
[6] Keck E., Armenkas A.E., 1971, Wave propagation in transversely isotropic layered cylinders, ASCE Journal of Engineering Mechanics 2: 541-555.
[7] Suvalov A.L., Poncelet O., Deschamps M., Baron C., 2005, Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates, Wave Motion 42: 367-382.
[8] Payton R.G., 1992, Wave propagation in a restricted transversely isotropic elastic solid whose slowness surface contains conical points, Quarterly Journal of Mechanics and Applied 45: 183-197.
[9] Slaughter W.S., 2002, The Linearized Theory of Elasticity, Birkhauser.
[10] Parfitt Eringen A.C., 1969, Reflection of Plane waves from the flat boundary of a micropolar elastic half-space, The Journal of Acoustical Society of America 45(5): 1258-1272.
[11] Kolsky H., 1963, Stress Waves in Solids, Clarendon Press, Oxford; Dover Press, New York.
[12] Brulin O., Hsieh R.K. T., 1981, Mechanics of Micropolar Media, World Scientific Publishing Corp. Pvt. Ltd., Singapore.
[13] Gauthier R.D., 1982, Experimental investigations on micropolar media, in: Mechanics of Micropolar Media, edited byO. Brulin, RKT Hsieh, World Scientific, Singapore.
