Abstract
A variational principle is formulated for coupled thermoelasticity for inhomogeneous media. The problem of thermoelastic energy dissipation accompanying transverse oscillations of an inhomogeneous isotropic cantilevered beam is solved.
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Abbreviations
- xs(s=1, 2, 3):
-
rectilinear Cartesian coordinates
- τ:
-
time
- λ tij (i, j=1, 2, 3):
-
coefficients of thermal conductivity of an anisotropic body
- t0 :
-
temperature of the body in an unstressed state
- t:
-
increase in temperature at points in the body
- S:
-
entropy
- eij :
-
components of the deformation in Cartesian numbered axes
- cijkι:
-
elastic coefficients of inhomogeneous anisotropic bodies
- βij :
-
coefficients of an inhomogeneous anisotropic body, taking into account the mechanical and thermal properties of the material
- ce :
-
volume heat capacity at constant deformation
- ρ:
-
density of the inhomogeneous anisotropic body
- Xi :
-
components of the vector of mass forces
- Pi :
-
components of the vector of surface forces
Literature cited
Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kiev (1976).
A. D. Kovalenko, Foundations of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1970).
Yu. M. Kolyano and Z. I. Shter, “Thermoelasticity of inhomogeneous media,” Inzh.-Fiz. Zh.,38, No. 6, 1111–1114 (1980).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 102–107, January, 1982.
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Kolyano, Y.M., Shter, Z.I. Application of the variational principle to the solution of generalized coupled problems in thermoelasticity of inhomogeneous media. Journal of Engineering Physics 42, 84–88 (1982). https://doi.org/10.1007/BF00824998
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DOI: https://doi.org/10.1007/BF00824998