International Applied Mechanics

, Volume 54, Issue 1, pp 85–93 | Cite as

Forced Vibrations and Dissipative Heating of Hinged Flexible Viscoelastic Rectangular Plates with Actuators Under Shear Deformation

  • V. G. Karnaukhov
  • V. N. Kozlov
  • T. V. Karnaukhova

The forced resonant vibrations and vibrational heating of viscoelastic plates with actuators are modeled considering geometrical nonlinearity and transverse shear. An approximate analytical solution of the problem is obtained for a hinged rectangular plate by the Bubnov–Galerkin method. The effect of geometrical nonlinearity and shear deformations on the efficiency of active damping of vibrations with piezoelectric actuators is analyzed.


resonant vibrations geometrical nonlinearity transverse shear piezoelectric actuators active damping 


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  1. 1.
    A. F. Bulat, V. I. Dyrda, V. G. Karnaukhov, E. L. Zvyagil’skii, and A. S. Kobets, Forced Vibrations and Dissipative Heating of Elastic Bodies, Vol. 3 of the four-volume series Applied Mechanics of Elastic-Hereditary Media [in Russian], Naukova Dumka, Kiev (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 Elements [in Russian], Naukova Dumka, Kiev (1989).Google Scholar
  3. 3.
    V. G. Karnaukhov and I. F. Kirichok, Electrothermoviscoelasticity, Vol. 4 of the five-volume series Mechanics of Coupled Fields in Structural Elements [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
  4. 4.
    V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermal Mechanics of Piezoelectric Inelastic Bodies under Monoharmonic Loading [in Russian], ZhGTU, Shitomir (2005).Google Scholar
  5. 5.
    V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Thermal failure of inelastic hinged rectangular plate with piezoelectric sensors and actuators under forced resonant bending vibrations,” Byul. Dnepropetrovsk Univ., Ser. Mekh., 2, No. 5 (15), 68–75 (2011).Google Scholar
  6. 6.
    V. V. Matveev Damping of Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kiev (1985)Google Scholar
  7. 7.
    A. N. Guz (ed.), Mechanics of Composites [in Russian], in 12 vols., A.S.K., Kiev (1992).Google Scholar
  8. 8.
    Yu. A. Mitropolsky, Nonlinear Mechanics, Single-Frequency Vibrations [in Russian], Inst. Mat. NAS Ukrainy, Kiev (1997).Google Scholar
  9. 9.
    A. Nashif, J. Jones, and J. Henderson, Vibrations Damping, New York, Wiley (1985).Google Scholar
  10. 10.
    Yu. N. Rabotnov, Elements of Hereditary Solid Mechanics [in Russian], Nauka, Moscow (1977).zbMATHGoogle Scholar
  11. 11.
    G. S. Agnes, “Development of a modal model for simultaneous active and passive piezoelectric vibration suppression,” J. Intell. Mater. Syst. Struct., 6, No. 4, 482–487 (1995).MathSciNetCrossRefGoogle Scholar
  12. 12.
    G. S. Bae, M. K. Kwak, and D. J. Inman, “Vibration suppression of a cantilever beam using eddy current of damper,” J. S. V., 284, No. 3–5, 805–814 (2005).Google Scholar
  13. 13.
    U. Gabbert and H. S. Tzou, Smart Structures and Structronic Systems, Kluwer Academic Pub., Dordrecht (2001).CrossRefGoogle Scholar
  14. 14.
    I. A. Guz, Y. A. Zhuk, and M. Kashtalyan, “Dissipative heating and thermal fatigue life prediction for structures containing piezoactive layers,” Techn. Mech., 32, No. 2–5, 238–250 (2012).Google Scholar
  15. 15.
    Mel Schwartz (ed.), Encyclopedia of Smart Materials, 1–2, Wiley & Sons, New York (2002).Google Scholar
  16. 16.
    D. I. Jones, Handbook of Viscoelastic Vibration Damping, Wiley & Sons, New York (2001).Google Scholar
  17. 17.
    J. F. He and D. A. Ma, “Analysis of flexural vibration of viscoellastically damped sandwich plates,” J. Sound Vibr., 126, No. 1, 37–47 (1988).ADSCrossRefGoogle Scholar
  18. 18.
    V. L. Karlash, “Influence of electric loading conditions on the vibrations of piezoceramic resonators,” Int. Appl. Mech., 53, No. 2, 220–227 (2017).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    V. L. Karlash, “Phase–frequency characteristics of the longitudinal and transverse vibrations of planar piezoceramic transformers,” Int. App. Mech., 53, No. 3, 349–355 (2017).MathSciNetCrossRefGoogle Scholar
  20. 20.
    V. L. Karlash, “Effect of split or partial electrodes on the forced vibrations of bear-type piezoceramic transducers”, Int. Appl. Mech., 52, No. 5, 535–546 (2016).ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    T. V. Karnaukhova, “Thermal depolarization of a piezoelectric layer under harmonic quasistatic electric loading,” Int. Appl. Mech., 34, No. 4, 373–376 (1998).MathSciNetzbMATHGoogle Scholar
  22. 22.
    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
  23. 23.
    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).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    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
  25. 25.
    I. F. Kirichok, “Damping the radial vibrations and self-heating of viscoelastic shell elements with piezoelectric sensor and actuator,” Int. Appl. Mech., 52, No. 4, 354–358 (2016).ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC, Boca Raton (2007).Google Scholar
  27. 27.
    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
  28. 28.
    H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers, Boston (1993).CrossRefGoogle Scholar
  29. 29.
    H. S. Tzou and L. A. Bergman, Dynamics and Control of Distributed Systems, Cambridge University Press, Cambridge (1998).CrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. G. Karnaukhov
    • 1
  • V. N. Kozlov
    • 1
  • T. V. Karnaukhova
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.National Technical University “KPI”KievUkraine

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