Advertisement

Basic relations of the theory of thermoviscoelastic plates with distributed sensors

  • T. V. Karnaukhova
  • E. V. Pyatetskaya
Article

The basic relations of the thermomechanics of thin-walled viscoelastic plates with distributed piezoelectric sensors under monogarmonic mechanical loading are presented. To describe the thermomechanical behavior of materials, the concept of complex characteristics is used. Numerical and variational methods are used to study the forced resonant vibrations of viscoelastic plates with distributed piezoelectric sensors. The effect of dissipative heating on the readings of the sensors of a circular viscoelastic plate undergoing axisymmetric resonant bending vibrations is analyzed as an example

Keywords

forced resonant vibrations thermoviscoelastic plate variational methods dissipative heating circular viscoelastic plate 

References

  1. 1.
    V. G. Karnaukhov, “Thermal failure of polymeric structural elements under monoharmonic deformation,” Int. Appl. Mech., 40, No. 6, 622–655 (2004).CrossRefMathSciNetGoogle Scholar
  2. 2.
    V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermomechanics of Piezoelectric Bodies under Monoharmonic Loading [in Russian], ZhTTU, Zhitomir (2005).Google Scholar
  3. 3.
    V. G. Karnaukhov and Ya. V. Tkachenko, “Damping the vibrations of a rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 44, No. 2, 182–187 (2008).CrossRefGoogle Scholar
  4. 4.
    T. V. Karnaukhova and E. V. Pyatetskaya, “Basic equations for thermoviscoelastic plates with distributed actuators under monoharmonic loading,” Int. Appl. Mech., 45, No. 2, 200–214 (2009).CrossRefGoogle Scholar
  5. 5.
    T. V. Karnaukhova and E. V. Pyatetskaya, “Damping the resonant flexural vibration of a hinged plate with actuators,” Int. Appl. Mech., 45, No. 4, 448–456 (2009).CrossRefGoogle Scholar
  6. 6.
    T. V. Karnaukhova and E. V. Pyatetskaya, “Damping the flexural vibration of a clamped viscoelastic rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 45, No. 5, 546–557 (2009).CrossRefGoogle Scholar
  7. 7.
    I. F. Kirichok, “Flexural vibrations and vibrational heating of a ring plate with thin piezoceramic pads under single-frequency electromechanical loading,” Int. Appl. Mech., 44, No. 2, 200–207 (2008).CrossRefGoogle Scholar
  8. 8.
    I. F. Kirichok, E. V. Pyatetskaya, and M. V. Karnaukhov, “Bending vibrations and dissipative heating of a circular viscoelastc plate with piezoelectric actuators under electromechanical monoharmonic loading,” Visn. Kyiv. Univ., Ser. Fiz. Mat. Nauky, No. 2, 84–92 (2006).Google Scholar
  9. 9.
    I. F. Kirichok and M. V. Karnaukhov, “Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading,” Int. Appl. Mech., 44, No. 1, 65–72 (2008).CrossRefGoogle Scholar
  10. 10.
    I. F. Kirichok and M. V. Karnaukhov, “Monoharmonic vibrations and vibrational heating of an electromechanically loaded circular plate with piezoelectric actuators subject to shear strain,” Int. Appl. Mech., 44, No. 9, 1041–1049 (2008).CrossRefGoogle Scholar
  11. 11.
    W. P. Mason (ed.), Physical Acoustics. Principles and Methods, Vol. 2, Part B. Properties of Polymers and Nonlinear Acoustics, Academic Press, New York–London (1965).Google Scholar
  12. 12.
    N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).Google Scholar
  13. 13.
    O. P. Chervinko, I. K. Senchenkov, and N. N. Yakimenko, “Vibrations and self-heating of a viscoelastic prism with cylindrical inclusion,” Int. Appl. Mech., 43, No. 6, 647–653 (2007).CrossRefGoogle Scholar
  14. 14.
    V. A. Dolya, O. P. Chervinko, and I. K. Senchenkov, “Vibrations and self-heating of a layered viscoelastic rectangular prism under a vibrating punch,” Int. Appl. Mech., 43, No. 8, 886–892 (2007).CrossRefGoogle Scholar
  15. 15.
    V. L. Karlash, “Planar electroelastic vibrations of a piezoceramic plate and a half-disk,” Int. Appl. Mech., 43, No. 5, 547–553 (2007).CrossRefGoogle Scholar
  16. 16.
    V. L. Karlash, “Evolution of the planar vibrations of a rectangular plate as its aspect ratio is changed,” Int. Appl. Mech., 43, No. 7, 786–793 (2007).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.National Technical University of Ukraine “KPI”KyivUkraine
  2. 2.Taras Shevchenko National UniversityKyivUkraine

Personalised recommendations