Research Article
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Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials

Year 2021, Volume: 24 Issue: 1, 275 - 282, 01.03.2021
https://doi.org/10.2339/politeknik.650808

Abstract

In this study, the frequency response of a pre-stressed slab, which stands on a rigid foundation, subject to a timely harmonic loading was considered. The investigation is implemented according to the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). The considered body was designed joining to three discrete slabs side-by-side. It was assumed that there exists a rigidly clamping state at all interface planes on the system. A mathematical model of the problem is constructed and the system related to equations of motion is numerically solved using the finite element method (FEM). Particularly, the effect the ratio of the layer length has on the frequency response of the slab was presented.     

Supporting Institution

Kastamonu Üniversitesi

Project Number

KÜBAP-01/2016-04

Thanks

The author would like to acknowledge the financial grant given by the Research Fund of Kastamonu University for this research through the project KÜBAP-01/2016-04.

References

  • [1] Guz A.N., “Fundamentals of the Three-dimensional Theory of Stability of Deformable Bodies”, (trans. from Russian by M. Kashtalian), Springer-Verlag, New York, (1999).
  • [2] Akbarov S.D., “Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites”, Springer-Verlag, New York, (2013).
  • [3] Akbarov S.D., “Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach”, Springer-Verlag, New York, (2015).
  • [4] Wen-tao H., Tang-dai X., Wei-yun C., “Influence of lateral initial pressure on axisymmetric wave propagation in hollow cylinder based on first power hypo-elastic model”, Journal of Central South University, 21(2): 753-760, (2014).
  • [5] Daşdemir A., Eröz M., “Mathematical modeling of dynamical stress field problem for a pre-stressed bi-layered plate-strip”, Bulletin of the Malaysian Mathematical Sciences Society, 38(2): 733-760, (2015).
  • [6] Daşdemir A., “Dynamic response of a pre-stressed bi-layered plate-strip subjected to an arbitrary inclined time-harmonic force”, Creative Mathematics and Informatics, 26(3): 255-262, (2017).
  • [7] Daşdemir A., “Effect of initial stress on the dynamic response of a multi-layered plate-strip subjected to an arbitrary inclined time-harmonic force”, International Journal of Applied Mechanics and Engineering, 22(3): 521-537, (2017).
  • [8] Sergienko I.V., Deineka V.S., “Numerical solution of the dynamic problem of elasticity for bodies with concentrated masses”, International Applied Mechanics, 40(12): 1360-1370, (2004).
  • [9] Akbarov S.D., Zamanov A.D., Suleimanov T.R., “Forced vibration of a prestretched two-layer slab on a rigid foundation”, Mechanics of Composite Materials, 41(3): 229-240, (2005).
  • [10] Zhuk Y.A., Guz I.A., “Features of propagation of plane waves along to the layers of an initially stressed nanocomposite material”, International Applied Mechanics, 43(4): 3-26, (2007).
  • [11] Pandit M.K., Singh B.N., Sheikh A.H., “Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory”, Thin-Walled Structures, 46(11): 1183-1191, (2008).
  • [12] Zienkiewicz O.C., Taylor R.L., “The Finite Element Method, Basic Formulation and Linear Problems”, McGraw-Hill, London, (1989).
  • [13] Uflyand Ya.S., “Integral Transformations in the Theory of Elasticity”, Nauka, Moscow-Leningrad, (1963).

Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials

Year 2021, Volume: 24 Issue: 1, 275 - 282, 01.03.2021
https://doi.org/10.2339/politeknik.650808

Abstract

In this study, the frequency response of a pre-stressed slab, which stands on a rigid foundation, subject to a timely harmonic loading was considered. The investigation is implemented according to the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). The considered body was designed joining to three discrete slabs side-by-side. It was assumed that there exists a rigidly clamping state at all interface planes on the system. A mathematical model of the problem is constructed and the system related to equations of motion is numerically solved using the finite element method (FEM). Particularly, the effect the ratio of the layer length has on the frequency response of the slab was presented.     

Project Number

KÜBAP-01/2016-04

References

  • [1] Guz A.N., “Fundamentals of the Three-dimensional Theory of Stability of Deformable Bodies”, (trans. from Russian by M. Kashtalian), Springer-Verlag, New York, (1999).
  • [2] Akbarov S.D., “Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites”, Springer-Verlag, New York, (2013).
  • [3] Akbarov S.D., “Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach”, Springer-Verlag, New York, (2015).
  • [4] Wen-tao H., Tang-dai X., Wei-yun C., “Influence of lateral initial pressure on axisymmetric wave propagation in hollow cylinder based on first power hypo-elastic model”, Journal of Central South University, 21(2): 753-760, (2014).
  • [5] Daşdemir A., Eröz M., “Mathematical modeling of dynamical stress field problem for a pre-stressed bi-layered plate-strip”, Bulletin of the Malaysian Mathematical Sciences Society, 38(2): 733-760, (2015).
  • [6] Daşdemir A., “Dynamic response of a pre-stressed bi-layered plate-strip subjected to an arbitrary inclined time-harmonic force”, Creative Mathematics and Informatics, 26(3): 255-262, (2017).
  • [7] Daşdemir A., “Effect of initial stress on the dynamic response of a multi-layered plate-strip subjected to an arbitrary inclined time-harmonic force”, International Journal of Applied Mechanics and Engineering, 22(3): 521-537, (2017).
  • [8] Sergienko I.V., Deineka V.S., “Numerical solution of the dynamic problem of elasticity for bodies with concentrated masses”, International Applied Mechanics, 40(12): 1360-1370, (2004).
  • [9] Akbarov S.D., Zamanov A.D., Suleimanov T.R., “Forced vibration of a prestretched two-layer slab on a rigid foundation”, Mechanics of Composite Materials, 41(3): 229-240, (2005).
  • [10] Zhuk Y.A., Guz I.A., “Features of propagation of plane waves along to the layers of an initially stressed nanocomposite material”, International Applied Mechanics, 43(4): 3-26, (2007).
  • [11] Pandit M.K., Singh B.N., Sheikh A.H., “Buckling of laminated sandwich plates with soft core based on an improved higher order zigzag theory”, Thin-Walled Structures, 46(11): 1183-1191, (2008).
  • [12] Zienkiewicz O.C., Taylor R.L., “The Finite Element Method, Basic Formulation and Linear Problems”, McGraw-Hill, London, (1989).
  • [13] Uflyand Ya.S., “Integral Transformations in the Theory of Elasticity”, Nauka, Moscow-Leningrad, (1963).
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Ahmet Daşdemir 0000-0001-8352-2020

Project Number KÜBAP-01/2016-04
Publication Date March 1, 2021
Submission Date November 25, 2019
Published in Issue Year 2021 Volume: 24 Issue: 1

Cite

APA Daşdemir, A. (2021). Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials. Politeknik Dergisi, 24(1), 275-282. https://doi.org/10.2339/politeknik.650808
AMA Daşdemir A. Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials. Politeknik Dergisi. March 2021;24(1):275-282. doi:10.2339/politeknik.650808
Chicago Daşdemir, Ahmet. “Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials”. Politeknik Dergisi 24, no. 1 (March 2021): 275-82. https://doi.org/10.2339/politeknik.650808.
EndNote Daşdemir A (March 1, 2021) Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials. Politeknik Dergisi 24 1 275–282.
IEEE A. Daşdemir, “Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials”, Politeknik Dergisi, vol. 24, no. 1, pp. 275–282, 2021, doi: 10.2339/politeknik.650808.
ISNAD Daşdemir, Ahmet. “Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials”. Politeknik Dergisi 24/1 (March 2021), 275-282. https://doi.org/10.2339/politeknik.650808.
JAMA Daşdemir A. Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials. Politeknik Dergisi. 2021;24:275–282.
MLA Daşdemir, Ahmet. “Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials”. Politeknik Dergisi, vol. 24, no. 1, 2021, pp. 275-82, doi:10.2339/politeknik.650808.
Vancouver Daşdemir A. Frequency Response of an Initially Stressed Slab Made from Three Compressible Materials. Politeknik Dergisi. 2021;24(1):275-82.