Free vibrations and seismic resistance of three-layer non-homogeneous orthotropic rectangular plates

Authors

  • Санан Низами оглы Гараисаев Azerbaijan University of Architecture and Construction Baku, A. Sultanov Str.5/Az1073, Azerbaijan

DOI:

https://doi.org/10.15587/1729-4061.2014.24866

Keywords:

three-layer, orthotropic plates, non-homogeneous, elasticity characteristics, vibration, amplitude-frequency characteristics

Abstract

The problem of seismic resistance and free vibration of three-layer non-homogeneous, orthotropic rectangular plates, which layers are made of various, continuously non-homogeneous materials, is considered in the paper. It is assumed that elasticity characteristics of the material for layers are continuous functions of the plate thickness coordinate. Using the Kirchhoff-Love hypothesis for the entire thickness of the element, the expressions for forces and moments were obtained, as well as integrated stiffness characteristics for the three-layer orthotropic plate under consideration were determined. In general form, equation systems of the plate motion in both exact and approximate formulations were obtained. In the approximate formulation of the problem, two motion equations of the problem with respect to the deflection and the stress function were obtained. For the case of the plate pin-edge fixing, the problem solution was made and the formula for determining free vibrations of the plate was found. When making numerical calculations, the elasticity characteristics of the material for layers were taken as linear in relation to the thickness coordinates. 

Author Biography

Санан Низами оглы Гараисаев, Azerbaijan University of Architecture and Construction Baku, A. Sultanov Str.5/Az1073

Doctorant

Department of Teoretickal and Construction mechanics

References

  1. Вольмир, А. С. Устойчивость деформируемых систем [Текст] / А. С. Вольмир. – М.; Наука, 1967. – 984 с.
  2. Ломакин, В. А. Теория упругости неоднородных тел [Текст] / Ломакин, В. А. – М., изд–во МГУ, 1978. – 245 с.
  3. Алфутов, Н. А. Расчеты многослойных пластин и оболочек из композиционных материалов [Текст] / Н. А.Алфутов, П. А. Зиновьев, Б. Г. Попов. – М.;Машиностроение, 1984. – 264 с.
  4. Rajasekaran, S. Stability and Vibration analysis of non-prismaticthin-walled composite spatial member sofgeneric section [Text] / S. Rajasekaran, K. Nalinaa // J.Appl.Mechanics. – 2010. – Vol. 77, № 3. – P. 310–319.
  5. Arshad, S. H. Vibration analysis of bilayered FGM cylindricalshells [Text] / S. H. Arshad, M. N. Naeem, N. Sultana, A. G. Shah, Z. Iqbal // J.Appl.Mechanics. – 2011. – Vol. 81, № 8. – P. 319–343.
  6. Viswanathan, K. K. Jang Hyun Lee. Zainal Abdul Aziz. Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness [Text] / K. K. Viswanathan, Jang Hyun Lee, Zainal Abdul Aziz //J.Acta Mechanica. – 2011. – Vol. 221, № 10. – P. 309–319.
  7. Alibeigloo, A. Free vibration analysis of nano-plate using three-dimensional theory of elasticity [Text] / A. Alibeigloo // J.Acta Mechanica. – 2011. – Vol. 222, № 11. – P. 149–159.
  8. Li, Peng The aeroelastic stability and bifurcation structure of subsonic nonlinear thin panels subjected to external excitation [Text] / Peng Li, Yiren Yang, Wei Xu, Guo Chen // J.Arch.Appl.Mech. – 2012. – Vol. 82. – P. 1251–1267.
  9. Avades, K. Free vibration analysis of laminated composite plates with elastical lyrestained edges using FEM [Text] / K. Avades, N. D. Sharma // CentralEuropeanJournalof Engineering. – 2013. – Vol. 3, № 2. – P. 306–315.
  10. Peng, Zhang Seismic Control of Power Transmission Tower Using Pounding TMD [Text] / Zhang Peng, Song Ganding, Li Hong-Nan, Lin You-Xin // J. Eng. Mech. – 2013. – Vol. 139 (10). – P. 1395–1406.
  11. Volmir, A. S. (1967). Stability of deformable systems. Moscow, USSR: Nauka, 984.
  12. Lomakin, V. A. (1978). The theory of elasticity of inhomogeneous bodies. Moscow, USSR: Moscov State University Press, 245.
  13. Alfutov, N. A., Zinoviev, P. A., Popov, B. G. (1984). Calculations of laminated plates and shells made of composite materials. Moscow, USSR: Mechanical Engineering, 264.
  14. Rajasekaran, S., Nalinaa, K. (2010). Stability and Vibration analysis of non-prismatic thin-walled composite spatial members of generic section, J. Appl. Mechanics, Vol. 77, № 3, 310–319.
  15. Arshad, S. H., Naeem, M. N., Sultana, N., Shah, A. G., Iqbal, Z. (2011). Vibration analysis of bilayered FGM cylindrical shells. J. Appl. Mechanics, Vol. 81 , № 8, 319–343.
  16. Viswanathan, K. K., Jang, Hyun Lee, Zainal, Abdul Aziz (2011). Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness. J. Acta Mechanica, Vol. 221, № 10, 309–319.
  17. Alibeigloo, A. (2011). Free vibration analysis of nano-plate using three-dimensional theory of elasticity. J.Acta Mechanica, Vol. 222, № 11, 149–159.
  18. Li, Peng, Yang, Yiren, Xu, Wei, Chen, Guo (2012). On the aeroelastic stability and bifurcation structure of subsonic nonlinear thin panels subjected to external excitation. J. Arch. Appl. Mech., 82, 1251–1267.
  19. Avades, K., Sharma, N. D. (2013). Free vibration analysis of laminated composite plates with elasticallyrestained edges using FEM. .Central European Journal of Engineering, Vol. 3, № 2, 306–315.
  20. Peng, Zhang, Gangbing, Song, Hong-Nan, Li, You-Xin, Lin (2013). Seismic Control of Power Transmission Tower Using Pounding TMD. J. Eng. Mech., Vol. 139, № 10, 1395–1406.

Downloads

Published

2014-06-20

How to Cite

Гараисаев, С. Н. о. (2014). Free vibrations and seismic resistance of three-layer non-homogeneous orthotropic rectangular plates. Eastern-European Journal of Enterprise Technologies, 3(7(69), 4–7. https://doi.org/10.15587/1729-4061.2014.24866

Issue

Vol. 3 No. 7(69) (2014): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2014 Санан Низами оглы Гараисаев

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.