Skip to main content
Log in

Forced Resonant Vibrations and Self-Heating of Solids of Revolution Made of a Viscoelastic Piezoelectric Material

  • Published:
International Applied Mechanics Aims and scope

The concept of complex characteristics is used to formulate the coupled nonlinear boundary-value thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of inelastic three-dimensional bodies of revolution taking into account the nonlinearity due to the dependence of the mechanical and electrical characteristics on temperature. An iteration method is used to reduce this nonlinear problem to a linear electroviscoelastic problem and a linear heat-conduction problem with a known heat source, which are solved using the finite-element method. This approach is used to solve a coupled nonlinear thermoelectroviscoelastic problem of the forced harmonic vibrations and self-heating of a hinged sandwich cylindrical panel. The numerical data obtained are analyzed, and the effect of nonlinearity on the amplitude–frequency and temperature–frequency responses is studied

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

Access this article

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. K. J. Bathe and E. L. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1976).

  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).

  3. V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermomechanics of Piezoelectric Inelastic Bodies under Monoharmonic Loading [in Russian], ZhTTU, Zhitomir (2005).

    Google Scholar 

  4. A. Yu. Grigorenko and I. A. Loza, “Nonaxisymmetric waves in layered hollow cylinders with axially polarized piezoceramic layers,” Int. Appl. Mech., 50, No. 2, 150–158 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  5. H. R. Hamidzadeh and R. N. Jazar, Vibrations of Thick Cylindrical Structurals, Springer, Heidelberg (2010).

    Book  Google Scholar 

  6. V. G. Karnaukhov, “Thermomechanics of coupled fields in passive and piezoactive inelastic bodies under harmonic deformation,” J. Therm. Stresses, 28, No. 6–7, 783–315 (2005).

    Article  Google Scholar 

  7. V. I. Kozlov, “Oscillation and dissipative heating of a multilayer shell of revolution made of viscoelatic material,” Int. Appl. Mech., 32, No. 6, 480–487 (1996).

    Article  ADS  MATH  Google Scholar 

  8. R. G. Sabat, B. Mukherjee, W. Ren, and G. Yung, “Temperature dependence of the complete material coefficients matrix of soft and hard doped piezoelectric lead zirconate titanate ceramics,” J. Appl. Phys., 101, No. 6, 64–111 (2007).

    Google Scholar 

  9. M. Schwartz, Encyclopedia of Smart Materials, Willey, Michigan (2002).

    Book  Google Scholar 

  10. N. A. Shu’lga, L. O. Grigor’eva, and A. A. Kirichenko, “Nonstationary electroelastic vibrations of a spherical shell with impedance boundary conditions,” Int. Appl. Mech., 50, No. 3, 274–281 (2014).

    Article  MathSciNet  Google Scholar 

  11. N. A. Shu’lga and V. V. Levchenko, “Natural modes of vibration of piezoelectric circular plates with radially cut electrodes,” Int. Appl. Mech., 50, No. 5, 582–592 (2014).

    Article  MathSciNet  Google Scholar 

  12. H. S. Tzou and L. A. Bergman, Dynamics and Control of Distributed Systems, Cambridge University Press, Cambridge (1998).

    Book  Google Scholar 

  13. H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer, Dordrecht (1993).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. G. Karnaukhov.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 51, No. 6, pp. 12–22, November–December 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karnaukhov, V.G., Kozlov, V.I., Zavgorodnii, A.V. et al. Forced Resonant Vibrations and Self-Heating of Solids of Revolution Made of a Viscoelastic Piezoelectric Material. Int Appl Mech 51, 614–622 (2015). https://doi.org/10.1007/s10778-015-0718-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-015-0718-2

Keywords

Navigation