Axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate

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

Abstrakty

EN

The propagation of axisymmetric free vibrations in a microstretch thermoelastic homogeneous isotropic plate subjected to stress free thermally insulated and isothermal conditions is investigated in the context of the conventional coupled thermoelasticity (CT) and Lord and Shulman (L-S) theories of thermoelasticity. The generalized theory of elasticity developed by Lord and Shulman is employed by assuming the mechanical behaviour as dynamic to study the problem. Mathematical modeling of the problem of obtaining dispersion curves for microstretch isotropic thermally conducting elastic plates leads to coupled differential equations. The model has been simplified by using the Helmholtz decomposition technique and the resulting equations have been solved by using the variable separable method to obtain the secular equations in isolated mathematical conditions for the plates with a stress free thermally insulated and isothermal boundary surface. The secular equations for both the symmetric and skew-symmetric wave mode propagation have been obtained. Thin plate results have also been deduced. These vibration modes are found to be dispersive and dissipated in character. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to the Rayleigh surface wave frequency equation. The dispersion curves, attenuation coefficients and amplitudes of dilatation, microrotation, microstretch and temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically for the Lord and Shulman theory of elasticity. The theoretical and numerical computations are found to be in close aggrement.

Słowa kluczowe

EN

microstretch; secular equations; phase velocity; attenuation coefficient

PL

prędkość fazowa; współczynnik tłumienia

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2009
• Tom: Vol. 14, no 1
• Strony: 211--237
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Kumar R.

autor

Partap G.

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

Bibliografia

• Biot M. (1956): Thermoelasticity and irreversible thermodynamics. - J. Appl. Phys., vol.27, pp.240-253.
• De Cicco S. (2003): Stress concentration effects in microstretch elastic solids. - Int. J. Eng. Sci., vol.41, pp.187-199.
• Eringen A.C. (1964): Mechanics of micromorphic materials. - Proceedings of the 11th International Congress of Applied Mechanics (H. Gortler, Ed.), Springer - Verlag, New York, pp.131-138.
• Eringen A.C. (1966): Linear theory of micropolar elasticity. - J. Math. Mech., vol.15, pp.909-923.
• Eringen A.C. (1968a): Theory of micropolar elasticity, In: H.Liebowitz (Ed.), Fracture. - Vol.2, Academic Press, New York, pp.621-729.
• Eringen A.C. (1968b): Mechanics of micromorphic continua. - IUTAM Symposium, Mechanics of Generalized Continua ( Kroner Ed.), Springer - Verlag, New York, pp.18-35.
• Eringen A.C. (1971): Micropolar elastic solids with stretch, In: Prof. Dr. Mustafa Inan Anisina, Ari Kitabevi Matbaasi, Istanbul, pp.1-18.
• Eringen A.C. (1990): Theory of thermo-microstretch elastic solids. - Int. J. Eng. Sci., vol.28, pp.1291-1301.
• Eringen A.C. (1999): Microcontinuum Field Theories I: Foundations and Solids. - New York: Springer-Verlag.
• Graff K.F. (1991): Wave motion in Elastic Solids. - New York: Dover Publications, Inc.
• Kumar R. and Deswal S. (2002): Wave propagation through cylindrical bore contained in a microstretch elastic medium. - Journal of Sound and Vibration, vol.250, pp.711-722.
• Kumar R. and Partap G. (2005): Reflection of plane waves in a heat flux dependent microstretch thermoelastic solid half space. - Int. J. Applied Mechanics and Eng., vol.10, pp.253-266.
• Kumar R. and Singh B. (1998): Wave propagation in a generalized thermo - microstretch elastic solid. - Int. J. Eng. Sci., vol.36, pp.891-912.
• Lamb H. (1917): On waves in an elastic plate. - Phil. Trans Roy Soc London, Ser. A, vol.93, pp.114-128.
• Liu X. and Hu G. (2004): Inclusion problem of microstretch continuum. - Int. J. Eng. Sci., vol.42, pp.849-860.
• Lord H.W. and Shulman Y. (1967): A generalized dynamical theory of thermoelasticity. - J. Mech. Phys. Solids, vol.15, pp.299-309.
• Svanadze M. (2004): Fundamental solution of the system of equations of steady oscillations in the theory of microstretch elastic solids. - Int. J. Eng. Sci., vol.42, pp.1897-1910.
• Tomer S.K. and Garg M. (2005): Reflection and transmission of waves from a plane interface between two microstretch solid half spaces. - Int. J. Eng. Sci., vol.43, pp.139-169.