We presented the model of parametric vibrations of the hinged rectangular thermoviscoelastic piezoelectric plate taking into account the shear strains and dissipative heating. A solution to this problem is reduced to the classic Mathieu equation. We studied the effect of the temperature of dissipative heating on the parametric vibrations of the plate.
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V. V. Bolotin, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco, CA (1964).
A. F. Bulat, V. I. Dyrda, V. G. Karnaukhov, E. L. Zvyagil’skii, and A. S. Kobets, Forced Vibrations and Self-Heating of Inelastic Bodies, Vol. 4 of the three-volume series Applied Mechanics of Hereditary Elastic Materials [in Russian], Naukova Dumka, Kyiv (2014).
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity [in Russian], Naukova Dumka, Kyiv (1989).
A. N. Guz (ed.), J. Kabelka, S. Markus, et al., Dynamics and Stability of Laminated Composites [in Russian], Naukova Dumka, Kyiv (1991).
V. G. Karnaukhov, Coupled Problems of Thermoviscoelasticity [in Russian], Naukova Dumka, Kyiv (1982).
V. G. Karnaukhov and I. F. Kirichok, Coupled Problems for Viscoelastic Plates and Shells [in Russian], Naukova Dumka, Kyiv (1986).
V. G. Karnaukhov and I. F. Kirichok, Electrothermoviscoelasticity [in Russian], Naukova Dumka, Kyiv (1988).
V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Thermal failure of a hinged inelastic rectangular plate with piezoelectric sensors and actuators during forced resonant flexural vibrations,” Visn. Dnipropetr. Univ., Ser. Mekh., 15, No. 2, No. 5, 68–75 (2011).
I. A. Guz, Y. A. Zhuk, and M. Kashtalyan, “Dissipative heating and thermal fatigue life prediction for structures containing piezoactive layers,” Technische Mechanik, 32, No. 2–5, 238–250 (2012).
T. V. Karnaukhova, “Thermal depolarization of a piezoelectric layer under a harmonic quasistatic electric loading,” Int. Appl. Mech., 34, No. 4, 373–376 (1998).
V. G. Karnaukhov, “Thermomechanics of coupled fields in passive and piezoactive inelastic bodies under harmonic deformations (review),” J. Therm. Stress, 28, No. 6–7, 783–815 (2005).
V. G. Karnaukhov, T. V. Karnaukhova, and O. McGillicaddy, “Thermal failure of flexible rectangular viscoelastic plates with distributed sensors and actuators,” J. Eng. Math., 78, No. 1, 199–212 (2013).
V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Forced vibrations and dissipative heating of hinged flexible viscoelastic rectangular plates with actuators under shear deformations,” Int. Appl. Mech., 54, No. 1. 85–93 (2018).
V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Influence of anisotropy and transverse-shear strains on the performance of piezoelectric sensors and actuators,” Int. Appl. Mech., 54, No. 3, 331–338 (2018).
V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Critical electric load on a hinged thermoviscoelastic rectangular plate with piezoelectric sensors and actuators,” Int. Appl. Mech., 55, No. 6, 596–600 (2019).
J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton (2007).
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This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Translated from Prikladnaya Mekhanika, Vol. 56, No. 3, pp. 84–89, May–June 2020.
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Karnaukhov, V.G., Kozlov, V.I. & Karnaukhova, T.V. Parametric Vibrations of a Hinged Thermoviscoelastic Rectangular Piezoelectric Plate with Shear Strains and Dissipative Heating Taken Into Account*. Int Appl Mech 56, 334–339 (2020). https://doi.org/10.1007/s10778-020-01015-9
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DOI: https://doi.org/10.1007/s10778-020-01015-9