Analysis of free vibrations for Rayleigh lamb waves in a micropolar viscoelastic plate

• Autorzy: Kumar R. , Partap G.
• Języki publikacji: EN

Abstrakty

EN

The propagation of free vibrations in a homogeneous isotropic micropolar viscoelastic plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. The regions of secular equations are obtained and special cases such as Lame modes, thin plate results and short wavelength waves are also discussed. At short wavelength limit, the secular equations for symmetric and skew symmetric waves in a stress free plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of normal force stress, tangential force stress and tangential couple stress are obtained and depicted graphically. Finally, numerical solution is carried out for magnesium crystal composite material plate.

Słowa kluczowe

EN

micropolar viscoelastic plate; secular equations; phase velocity; attenuation coefficients; amplitudes

PL

fala Rayleigha; częstotliwość fal; przepływ płynu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2008
• Tom: Vol. 13, no 2
• Strony: 383--397
• Opis fizyczny: Bibliogr. 14 poz., wykr.

Twórcy

autor

Kumar R.

autor

Partap G.

• Department of Mathematics, Kurukshetra University Kurukshetra 136119, Haryana, INDIA,

Bibliografia

• Biswas P.K., Sengupta P.R. and Debnath L. (1996): Axisymmetric Lamb's problem in a semi-infinite micropolar viscoelastic medium. - Int. Math. Math. Sci., vol.19, pp.815-820.
• De Cicco S. and Nappa L. (1998): On Saint's Venant's principle for micropolar viscoelastic bodies. - Bit. J. Eng. Sci., vol.36, pp.883-893.
• EI-Karamany Ahmed S. (2003): Uniqueness and reciprocity theorems in generalized linear micropolar thermoviscoelasticity. - Int. J. Eng. Sci., vol.40, pp.2097-2117.
• Eringen A.C. (1966a): Linear theory of micropolar elasticity. - J. Math-Mech., vol.15, pp.909-923.
• Eringen A.C. (1966b): Theory of micropolar fluids. - J. Math-Mech., vol.16, pp.1-18.
• Eringen A.C. (1967): Linear theory of micropolar viscoelasticity. - Int. J. Eng. Sci., vol.5, pp.191-204.
• Eringen A.C. (1976): Non-local polar field theories in continuum physics. - New York: Academic Press, pp.205-267.
• Graff K.F. (1991): Wave motion in Elastic Solids. - New York: Dover publications, Inc..
• Kumar R., Gogna M.L. and Debnath L. (1990): Lamb's plane problem in micropolar viscoelastic half space with stretch. - Int. J. Math. And Sci., vol.13, pp.363-372.
• Kumar R. and Singh B. (2000): Reflection of plane waves at a planar viscoelastic micropolar interface. - Indian J. Pure and Applied Math., vol.31, pp.287-303.
• Kumar R. (2000): Wave propagation in a micropolar viscoelastic generalized thermoelastic solid. - Int. J. Eng. Sci., vol.38, pp.1377-1395.
• Kumar R. and Singh R. (2005): Elastodynamics of an axisymmetric problem in microstretch viscoelastic solid. - Int. J. Applied Mechanics and Engineering, vol.10, pp.227-244.
• Lamb H. (1917): On waves in an elastic plate. - Phil. Trans. Roy. Soc., London, Ser. A, vol.93, pp.114-128.
• McCarthy M.F. and Eringen A.C. (1969): Micropolar viscoelastic waves. - Int. J. Eng. Sci., vol.7, pp.447-458.