Skip to main content
SpringerLink
Log in

Thermal failure of flexible rectangular viscoelastic plates with distributed sensors and actuators

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Abstract

The problem of thermal failure of simply supported flexible rectangular plates with distributed sensors and actuators as a result of dissipative heating by forced resonant bending vibrations is considered. The plates are loaded by a uniformly distributed, harmonic-in-time pressure. The mechanical problem is solved by the Galerkin method and the method of harmonic balance. The influence of dissipative heating on the efficiency of active damping of the forced resonant vibrations of the flexible plates is investigated. By equating the temperature to the Curie point, a simple expression for the critical mechanical load is obtained. When the load is more this critical value the active materials lose the piezoelectric effect and become passive. This is a specific type of thermal failure, where the body keeps its integrity but the electromechanical system loses its functionality.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jones DIG (2001) Handbook of viscoelastic vibration damping. Wiley, New York

    Google Scholar 

  2. Tzou HS, Bergman LA (1998) Dynamics and control of distributed systems. Cambridge University Press, Cambridge

    Book  Google Scholar 

  3. Iljushin AA, Pobedrja BE (1970) Mathematical basics of the theory of thermo-visco-elasticity. Nauka-Verlag, Moscow

    Google Scholar 

  4. Birman V (1996) Thermal effects on measurements of dynamic processes in composite structures using piezoelectric sensors. Smart Mater Struct 5: 379–385

    Article  ADS  Google Scholar 

  5. Lu X, Hanagud SV (2004) Extended irreversible thermodynamics modeling for self-heating and dissipation in piezoelectric ceramics. IEEE Trans Ultrason Ferroelectr Freq Control 51: 1582–1592

    Article  Google Scholar 

  6. Mauk LD, Lynch CS (2003) Thermo-electro-mechanical behavior of ferroelectric materials. Part I: a computational micromechanical model versus experimental results. J Intell Mater Syst Struct 14: 587–602

    Article  Google Scholar 

  7. Mauk LD, Lynch CS (2003) Thermo-electro-mechanical behavior of ferroelectric materials. Part II: introduction of rate and self-heating effects. J Intell Mater Syst Struct 14: 605–620

    Article  Google Scholar 

  8. Karnaukhov VG (2005) Thermomechanics of coupled fields in passive and piezoactive inelastic bodies under harmonic deformations. J Therm Stress 28: 783–815

    Article  Google Scholar 

  9. Karnaukhov VG, Kirichok IF, Karnaukhov MV (2008) The influence of dissipative heating on active vibration damping of viscoelastic plates. J Eng Math 61: 399–411

    Article  MATH  Google Scholar 

  10. Karnaukhova TV, Pyatetskaya EV (2009) Damping the flexural vibration of a clamped viscoelastic rectangular plate with piezoelectric actuators. Int Appl Mech 45: 546–557

    Article  MathSciNet  Google Scholar 

  11. Karnaukhova TV, Pyatetskaya EV (2009) Basic relations of the theory of thermoviscoelastic plate with distributed sensors. Int Appl Mech 45: 660–669

    Article  MathSciNet  Google Scholar 

  12. Karnaukhov VG, Kirichok IF (1986) Coupled problems of theory of viscoelastic plates and shells. Naukova Dumka, Kiev

    MATH  Google Scholar 

  13. Thomas O, Bilbao S (2008) Geometrically nonlinear flexural vibrations of plates: in-plane boundary conditions and some symmetry properties. J Sound Vib 315: 569–590

    Article  ADS  Google Scholar 

  14. Belouettar S, Azrar L, Daya EM, Laptev V, Potier-Ferry M (2008) Active control of nonlinear vibration of sandwich piezoelectric beams: a simplified approach. Comput Struct 86: 386–397

    Article  Google Scholar 

  15. Daya EM, Azrar L, Potier-Ferry M (2004) An amplitude equation for the nonlinear vibration of viscoelastically damped sandwich beams. J Sound Vib 271: 789–813

    Article  ADS  Google Scholar 

  16. Azrar L, Belouettar S, Wauer J (2008) Nonlinear vibration analysis of actively loaded sandwich piezoelectric beams with geometric imperfections. Comput Struct 86: 2182–2191

    Article  Google Scholar 

  17. Esmaizadeh E, Lalali MF (1999) Nonlinear oscillations of viscoelastic rectangular plates. Nonlinear Dyn 18: 311–319

    Article  Google Scholar 

  18. Kapuria S, Dumir PC (2005) Geometrically nonlinear axisymmetric response of thin circular plate under piezoelectric actuation. Commun Nonlinear Sci Numer Simul 10: 411–423

    Article  ADS  MATH  Google Scholar 

  19. Sun YX, Zhang SY (2001) Chaotic dynamic analysis of viscoelastic plates. Int J Mech Sci 43: 1195–1208

    Article  MATH  Google Scholar 

  20. Raouf RA (1993) A qualitative analysis of the nonlinear dynamic characteristics of curved orthotropic panels. Compos Eng 3: 1101–1110

    Article  Google Scholar 

  21. Kurpa L, Pilgun G, Amabili M (2007) Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments. J Sound Vib 306: 580–600

    Article  ADS  Google Scholar 

  22. Amabili M (2008) Nonlinear vibrations and stability of shells and plates. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  23. Karnaukhov VG, Mikhailenko VV (2005) Nonlinear thermomechanics of piezoelectric inelastic bodies under monoharmonic loading. Zhitomir Inzh Tekhnol Inst, Zhitomir (Monograph)

  24. Ambartsumyan SA (1967) Theory of anisotropic plates. Nauka, Moscow

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics of National Academy of Science of Ukraine, Nesterov Str., Kiev, 03057, Ukraine

    V. G. Karnaukhov, T. V. Karnaukhova & O. McGillicuddy

Authors
  1. V. G. Karnaukhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. V. Karnaukhova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. McGillicuddy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Karnaukhov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karnaukhov, V.G., Karnaukhova, T.V. & McGillicuddy, O. Thermal failure of flexible rectangular viscoelastic plates with distributed sensors and actuators. J Eng Math 78, 199–212 (2013). https://doi.org/10.1007/s10665-011-9514-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10665-011-9514-0

Keywords

Search

Navigation