The problem of forced resonant vibrations and dissipative heating of a hinged viscoelastic elastomeric plate under membrane preloads is given. The case of square and rectangular plates is considered. The effect of elastomer properties, preload, and heat exchange conditions on the amplitude- and temperature–frequency characteristics of the forced vibrations of the plate and the achievement of critical temperature at which the material softens is studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. H. Donnell, Beams, Plates, and Shells, McGraw Hill, New York (1976).
V. G. Karnaukhov and I. F. Kirichok, Coupled Problems for Viscoelastic Plates and Shells [in Russian], Naukova Dumka, Kyiv (1986).
V. G. Karnaukhov and B. P. Gumenyuk, Thermomechanics of Prestrained Viscoelastic Bodies [in Russian], Naukova Dumka, Kyiv (1990).
V. G. Karnaukhov, I. K. Senchenkov, and B. P. Gumenyuk, Thermomechanical Behavior of Viscoelastic Bodies under Harmonic Loading [in Russian], Naukova Dumka, Kyiv (1985).
V. G. Karnaukhov, I. K. Senchenkov, and O. P. Chervinko, “Influence of preliminary strain on the resonant vibrations and dissipative heating of a viscoelastic cylinder of finite length,” Int. Appl. Mech., 33, No. 1, 39–42 (1997).
V. N. Poturaev (ed.), V. I. Dyrda, V. G. Karnaukhov, et al., Thermomechanics of Elastomeric Structural Members under Cyclic Loading [in Russian], Naukova Dumka, Kyiv (1987).
V. W. Anderson and B. J. Lazan, Damping and Fatigue Properties of Magnesium and Magnese-Copper Alloys Proposed as New High Damping Materials, Internal rept., Aero Library, Minnesota (1957).
R. Behnke and M. Kalishke, “Thermo-mechanically coupled investigation of steady state rolling tires by numerical simulation and experiment,” Int. J. Non-Lin. Mech., No. 68, 101–131 (2015).
A. F. Bulat, V. I. Dyrda, and V. G. Karnaukhov, “Durability of thermoviscoelastic bodies under long-term cyclic loading,” Int. App. Mech., 55, No. 5, 495–503 (2019).
A. E. Green, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon Press, Oxford (1960).
M. Hashemi and Y. Zhuk, “The influence of strain amplitude, temperature and frequency on complex shear moduli of polymer materials under kinematic harmonic loading,” Mech. Mech. Eng., 21, No. 1, 157–170 (2017).
M. Hashemi and Y. A. Zhuk, Thermomechanical Stability and Thermal Fatigue Failure of Nanocomposite Structural Elements under Static and Cyclic Loading, Lambert Academic Publishing, (2018).
M. Hashemi and Y. A. Zhuk, “The influence of temperature on the cyclic properties of the transversely isotropic nanocomposite system under kinematic harmonic loading,” J. of Math. Sci., 236, No. 2, 185–198 (2019).
V. G. Karnaukhov and I. F. Kirichok, “Forced harmonic vibrations and dissipative heating-up of viscoelastic thin-walled elements (review),” Int. Appl. Mech., 36, No. 2, 174–195 (2000).
V. G. Karnaukhov, I. F. Kirichok, and V. I. Kozlov, “Electromechanical vibrations and dissipative heating of viscoelastic thin-walled piezoelements (review),” Int. Appl. Mech., 37, No. 2, 182–212 (2001).
V. G. Karnaukhov, I. F. Kirichok, and V. I. Kozlov, “Thermomechanics of inelastic thin-walled structural members with piezoelectric sensors and actuators under harmonic loading (review),” Int. Appl. Mech., 53, No. 1, 6–58 (2017).
B. Lazan, Damping of Materials and Members in Structural Mechanics, Pergamon Press, Oxford (1968).
C. J. Liu, Z. L. Zheng, X. Y. Yang, and J. J. Guo, “Geometric nonlinear vibration analysis for pretensioned rectangular orthotropic membrane,” Int. App. Mech., 54, No. 1, 104–119 (2018).
A. D. Nashif, D. I. Jones, and J. P. Henderson, Vibration Damping, Wiley-Interscience Publication, New York (1985).
J. C. Snowdon, Vibration and Shock in Damped Mechanical Systems, The Pensylvania State University, New York (1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 56, No. 4, pp. 47–60, July–August 2020.
This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Rights and permissions
About this article
Cite this article
Zhuk, Y.A., Ostos, A.K. Effect of Preloading on the Resonant Vibrations and Dissipative Heating of a Rectangular Thermoviscoelastic Plate*. Int Appl Mech 56, 432–444 (2020). https://doi.org/10.1007/s10778-020-01027-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-020-01027-5