Abstract
The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined
Similar content being viewed by others
References
T. Alfrey, Jr., Mechanical Behavior of High Polymers, Interscience, New York (1948).
V. G. Karnaukhov, Coupled Problem of Thermoviscoelasticity [in Russian], Naukova Dumka, Kyiv (1982).
V. G. Karnaukhov and I. K. Senchenkov, “Approximation methods for calculating critical thermal states,” Int. Appl. Mech., 12, No. 4, 340–346 (1976).
H. B. Keller, “Some positone problems suggested by nonlinear heat generation,” in: J. B. Keller and St. Antman (eds.), Bifurcation Theory and Nonlinear Eigenvalue Problems, WA Benjamin, New York (1969), pp. 217–255.
I. A. Motovilovets and V. I. Kozlov, Thermoelasticity, Vol. 1 of the six-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Kyiv (1987).
I. Narisawa, Strength of Polymeric Materials [Russian translation], Khimiya, Moscow (1987).
N. P. Nesterenko and I. K. Senchenkov, “Modeling vibrational heating of reinforced polymer films during ultrasonic welding with normal excitation,” in: Proc. 11th Int. Conf. on Mathematical Simulation and Information Technologies in Welding and Related Processes (Katsiveli, September 13–17, 2004) [in Russian], Inst. Élektrosvarki im. E. O. Patona NAN Ukrainy (1982), pp. 200–204.
N. P. Nesterenko, O. P. Chervinko, and I. K. Senchenkov, “Modelling ultrasonic heating of a fibrous composite cell under kinematic shear loading,” Sistemn. Tekhnol., Dnepropetrovsk, No. 4, 120–123 (2002).
N. P. Nesterenko, O. P. Chervinko, and I. K. Senchenkov, “Modeling ultrasonic heating of structural elements of fiber-reinforced polymer composites under normal loading,” Vest. Nats. Tekhn. Univ. KhPI, No. 9, 3–8 (2002).
Yu. S. Lipatov (ed.), Thermophysical and Rheological Characteristics of Polymers: A Handbook [in Russian], Naukova Dumka, Kyiv (1977).
V. N. Poturaev (ed.), V. I. Dyrda, V. G. Karnaukhov, et al., Thermomechanics of Elastomer Structural Members under Cyclic Loading [in Russian], Naukova Dumka, Kyiv (1987).
J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York (1970).
O. P. Chervinko, I. K. Senchenkov, and E. V. Dolya, “Calculating thermal instability parameters for a laminated prism,” Teor. Prikl. Mekh., 40, 63–67 (2005).
R. A. Schapery, “Effect of cyclic loading on the temperature in viscoelastic media with variable properties,” AIAA J., 2, No. 5, 827–835 (1964).
R. A. Schapery, “Thermomechanical behavior of viscoelastic media with variable properties subjected to cyclic loading,” Trans. ASME, Ser. E, Appl. Mech., 32, No. 3, 150–161 (1965).
O. P. Chervinko, “Calculation of the critical parameters characterizing the thermal instability of a viscoelastic prism with a stress concentrator under harmonic compression,” Int. Appl. Mech., 40, No. 8, 916–922 (2004).
V. G. Karnaukhov, “On A. D. Kovalenko’s research works on the thermomechanics of coupled fields in materials and structural members and its further development,” Int. Appl. Mech., 41, No. 9, 967–975 (2005).
V. G. Karnaukhov, “Thermal failure of polymeric structural elements under monoharmomc deformation,” Int. Appl. Mech., 40, No. 6, 622–655 (2004).
V. G. Karnaukhov, “Thermomechanics of the coupled fields in the passive and piezoactive inelastic bodies under the harmonic deformation,” in: Proc. 6th Int. Congr. on Thermal Stresses, 1, Vienna, Austria, May (2005), pp. 29–34.
V. G. Karnaukhov and I. F. Kirichok, “Vibrations and dissipative heating of a viscoelastic beam under a moving load,” Int. Appl. Mech., 41, No. 1, 49–55 (2005).
V. G. Karnaukhov and Yu. V. Revenko, “Dissipative heating of viscoelastic cylinder under a load steadily moving over its surface,” Int. Appl. Mech., 41, No. 2, 129–136 (2005).
V. G. Karnaukhov and Yu. V. Revenko, “Vibrations and dissipative heating of a viscoelastic cylindrical panel under a periodic moving load,” Int. Appl. Mech., 41, No. 4, 426–434 (2005).
A. Malinary and Y. Germain, “Self heating and thermal failure of polymers sustaining a compressive cyclic loading,” Int. J. Solid. Struct., 33, No. 23, 3439–3462 (1996).
R. W. Penn, “Dynamic mechanical properties of crystalline linear polyethylene,” J. Polym. Sci., No. 4, Pt. 2, 545–557 (1966).
I. K. Senchenkov, Ya. A. Zhuk, and V. G. Karnaukhov, “Modeling the thermomechanical behavior of physically nonlinear materials under monoharmomc loading,” Int. Appl. Mech., 40, No. 9, 943–969 (2004).
I. F. Tormey and S. C. Britton, “Effect of cyclic loading on solid propellant grain structures,” AIAA J., 1, No. 8, 3–7 (1963).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 73–81, June 2007.
Rights and permissions
About this article
Cite this article
Chervinko, O.P., Senchenkov, I.K. & Yakimenko, N.N. Vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion. Int Appl Mech 43, 647–653 (2007). https://doi.org/10.1007/s10778-007-0063-1
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-007-0063-1