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Critical Electric Load on a Hinged Thermoviscoelastic Rectangular Plate with Piezoelectric Sensors and Actuators*

  • V. G. KarnaukhovEmail author
  • V. I. Kozlov
  • T. V. Karnaukhova
Article
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We proposed a failure criterion for the system of controlling the forced vibration of a hinged rectangular thermoviscoelastic plate with piezoelectric sensors and actuators. This criterion is associated with the self-heating temperature reaching some critical value. The critical electric load is found on the basis of this criterion.

Keywords

thermoviscoelastic plate sensors and actuators vibrations self-heating critical electric load 

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References

  1. 1.
    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).Google Scholar
  2. 2.
    V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).Google Scholar
  3. 3.
    A. N. Guz (ed.), J. Kabelka, S. Markus, et al., Dynamics and Stability of Laminated Composites [in Russian], Naukova Dumka, Kyiv (1991).Google Scholar
  4. 4.
    V. G. Dubenets and V. V. Khil’chevskii, Vibrations of Damped Composite Structures [in Russian], Vol. 0.1, Vyshcha Shkola, Kyiv (1995).Google Scholar
  5. 5.
    V. G. Karnaukhov, Coupled Problems of Thermoviscoelasticity [in Russian], Naukova Dumka, Kyiv (1982).Google Scholar
  6. 6.
    V. G. Karnaukhov and I. F. Kirichok, Coupled Problems for Viscoelastic Plates and Shells [in Russian], Naukova Dumka, Kyiv (1986).zbMATHGoogle Scholar
  7. 7.
    V. G. Karnaukhov and I. F. Kirichok, Electrothermoviscoelasticity, Vol. 4 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1988).Google Scholar
  8. 8.
    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. Mekhanika, 15, No. 2, No. 5, 68–75 (2011).Google Scholar
  9. 9.
    V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Influence of shear strains on the effectiveness of piezoelectric sensors and actuators in active damping of the resonant vibrations of inelastic plates and shells,” Opir. Mater. Teor. Sporud, No. 95, 75–95 (2015).Google Scholar
  10. 10.
    V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermomechanics of Piezoelectric Inelastic Bodies under Monoharmonic Loading [in Russian], ZhGTU, Zhitomir (2005).Google Scholar
  11. 11.
    V. V. Matveev, Damping the Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kyiv (1985).Google Scholar
  12. 12.
    A. N. Guz (ed.), Mechanics of Composite Materials [in Russian], A.S.K., Kyiv (1992–2005).Google Scholar
  13. 13.
    Yu. A. Mitropolsky and B. I. Moseenkov, Asymptotic Solutions of Partial Differential Equations [in Russian], Vyshcha Shkola, Kyiv (1976).Google Scholar
  14. 14.
    Yu. A. Mitropolsky, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kyiv (1971).Google Scholar
  15. 15.
    Yu. A. Mitropolsky, Nonlinear Mechanics. Single-Frequency Vibrations [in Russian], Inst. Mat. NAN Ukrainy, Kyiv (1997).Google Scholar
  16. 16.
    A. D. Nashif, D. J. Johnes, and J. P. Henderson, Vibration Damping, John Wiley & Sons, New York (1985).Google Scholar
  17. 17.
    Y. N. Rabotnov, Elements of Hereditary Solid Mechanics, Mir, Moscow (1980).zbMATHGoogle Scholar
  18. 18.
    E. V. Savchenko, Passive Damping of Vibrations of Composite Structures [in Russian], Aspekt-Poligraf, Nezhin (2006).Google Scholar
  19. 19.
    N. A. Shul’ga and V. L. Karlash, Resonant Electromechanical Vibrations of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kyiv (2008).Google Scholar
  20. 20.
    U. Gabbert and H. S. Tzou, Smart Structures and Structronic Systems, Kluwer Academic Pub., Dordrecht (2001).CrossRefGoogle Scholar
  21. 21.
    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).Google Scholar
  22. 22.
    Encyclopedia of Smart Materials. In 2 vols, John Wiley and Sons, New York (2002).Google Scholar
  23. 23.
    D. I. Jones, Handbook of Viscoelastic Vibration Damping, John Wiley and Sons, New York (2001).Google Scholar
  24. 24.
    T. V. Karnaukhova, “Thermal depolarization of a piezoelectric layer under a harmonic quasistatic electric loading,” Int. Appl. Mech., 34, No. 4, 373–376 (1998).MathSciNetzbMATHGoogle Scholar
  25. 25.
    T. V. Karnaukhova, “Forced vibrations and dissipative heating of a hinged bimorph rectangular plate with open electrodes,” Int. Appl. Mech., 54, No. 2, 207–212 (2018).ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    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).CrossRefGoogle Scholar
  27. 27.
    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).MathSciNetCrossRefGoogle Scholar
  28. 28.
    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, 6–59 (2017).ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Thermal failure of flexible rectangular viscoelastic plates with distributed sensors and actuators,” Int. Appl. Mech., 54, No. 1, 85–93 (2018).ADSCrossRefGoogle Scholar
  30. 30.
    J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, Taylor and Francis, Boca Raton (2007).Google Scholar
  31. 31.
    J. Tani, T. Takagi, and J. Qui, “Intelligent material systems: application of functional materials,” Appl. Mech. Rev., 51, No. 8, 505–521 (1998).ADSCrossRefGoogle Scholar
  32. 32.
    H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers, Dordrecht (1993).CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. G. Karnaukhov
    • 1
    Email author
  • V. I. Kozlov
    • 1
  • T. V. Karnaukhova
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.National Technical University of Ukraine “KPI”KyivUkraine

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