Abstract
A dynamic boundary-value problem of coupled thermoelasticity for a finite cylinder with mixed boundary conditions is solved. The problem is reduced to a system of four singular integral equations solved by the mechanical-quadrature method. A numerical experiment is conducted to obtain amplitude-frequency characteristics for finite cylinders with different cross sections. The effect of thermoelastic coupling on stress distribution is assessed
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Bondar’, “The exact solution of a dynamic problem of coupled thermoelasticity (antisymmetric case),” in: Proc. Int. Sci. Conf. on Mathematical Problems in Engineering Mechanics [in Ukrainian], Dnepropetrovsk, April 19–22 (2005), p. 71.
P. Yu. Borodin, M. P. Galanin, and I. V. Dubovitskii, “Numerical solution for a layered elastic medium under impulsive thermal load: Spherically symmetric and plane cases,” in: Preprint No. 41, Inst. Prikl. Mat. RAN, Moscow (1997), pp. 1–29.
V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).
I. I. Vorovich and O. S. Malkina, “Stress state of a thick plate,” Prikl. Mat. Mekh., 31, No. 2, 230–241 (1967).
V. F. Gribanov and N. R. Panichkin, Coupled and Dynamic Problems of Thermoelasticity [in Russian], Mashinostroenie, Moscow (1984).
V. I. Danilovskaya, “Thermal stresses in an elastic half-space with abruptly heated boundary,” Prikl. Mat. Mekh., 14, No. 316–318 (1950).
V. G. Karnaukhov, Coupled Problems of Thermoviscoelasticity [in Russian], Naukova Dumka, Kyiv (1982).
A. D. Kovalenko, Thermoelasticity [in Russian], Vyshcha Shkola, Kyiv (1975).
A. S. Kosmodamianskii and V. A. Shaldyrvan, Thick Multiply Connected Plates [in Russian], Naukova Dumka, Kyiv (1978).
R. Kushnir, Ya. Maksimovich, and T. Solyar, “Thermoelastic state of multiply connected plates losing heat,” Mashinoznavstvo, No. 3 (81), 13–17 (2004).
M. A. Lavrent’ev and B. V. Shabat, Methods of Complex-Variable Theory [in Russian], Nauka, Moscow (1973).
A. I. Lurie, “Thick plate theory revisited,” Prikl. Mat. Mekh., 6, No. 2/3, 151–169 (1942).
A. V. Lykov, Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1967).
M. V. Molotov and I. D. Kil’, “Coupled dynamic problem of thermoelasticity for a half-space,” Prikl. Mat. Mekh., 60, No. 4, 687–696 (1996).
Ya. S. Podstrigach and Yu. M. Kolyano, Generalized Thermomechanics [in Russian], Naukova Dumka, Kyiv (1976).
V. K. Prokopov, “Review of studies on homogeneous solutions in the theory of elasticity and their applications,” Tr. Leningr. Politekhn. Inst., 279, 31–46 (1967).
L. A. Fil’shtinskii, “Tension of a layer with tunnel cuts,” Prikl. Mat. Mekh., 59, No. 5, 827–835 (1995).
L. Fil’shtinskii and O. Bondar, “Coupled thermoelastic fields in a layer subject to concentrated excitation (skew-symmetric solution),” Mashynoznavstvo, No. 5 (84), 30–38 (2004).
L. A. Fil’shtinskii and A. Ibeda, “Stationary wave process in an elastic layer with a cavity,” Vestn. DonGU, Ser. A, No. 1, 72–79 (2003).
H. Cho, G. A. Kardomateas, and C. S. Valle, “Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell,” Trans. ASME, J. Appl. Mech., 65, No. 1, 184–193 (1998).
L. A. Fil’shtinskii, Yu. D. Kovalev, and E. S. Ventsel, “Solution of the elastic boundary-value problems for a layer with tunnel stress raisers,” Int. J. Solids Struct., No. 39, 6385–6402 (2002).
L. A. Fil’shtinskii and Yu. D. Kovalev, “Solving the three-dimensional elastic problem for a cylinder of finite length subject to bending,” Int. Appl. Mech., 40, No. 5, 532–536 (2004).
Ya. M. Grigorenko and L. S. Rozhok, “Stress analysis of orthotropic hollow noncircular cylinders,” Int. Appl. Mech., 40, No. 6, 679–685 (2004).
Ya. M. Grigorenko and L. S. Rozhok, “Stress solution for transversely isotropic corrugated hollow cylinders,” Int. Appl. Mech., 41, No. 3, 277–282 (2005).
V. G. Karnaukhov, “Thermal failure of polymeric structural elements under monoharmonic deformation,” Int. Appl. Mech., 40, No. 6, 622–655 (2004).
V. G. Karnaukhov and Yu. V. Revenko, “Dissipative heating of a viscoelastic cylinder under a load steadily moving over its surface,” Int. Appl. Mech., 41, No. 2, 129–136 (2005).
W. S. Kim, L.G. Hector, Jr., and R. B. Hetnarski, “Thermoelastic stresses in a bounded layer due to repetitively pulsed laser radiation,” Acta Mech., 125, No. 1–4, 107–128 (1997).
C. S. Suh and C. P. Burger, “Effects of thermomechanical coupling and relaxation times on wave spectrum in dynamic theory of generalized thermoelasticity,” Trans. ASME, J. Appl. Mech., 65, No. 3, 605–613 (1998).
N. Sumi, “Propagation of thermal and thermal stress waves in finite medium under laser-pulse heating,” Trans Jap. Soc. Mech. Eng., 64, No. 625, 2257–2262 (1998).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 86–95, October 2006.
Rights and permissions
About this article
Cite this article
Fil’shtinskii, L.A., Bondar’, A.V. Influence of the coupling of mechanical and thermal fields on the amplitude-frequency characteristics of a cylinder. Int Appl Mech 42, 1151–1159 (2006). https://doi.org/10.1007/s10778-006-0187-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-006-0187-8