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Time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane

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Abstract

The time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and orthotropic half-plane is studied within the scope of the piecewise homogeneous body model utilizing the three-dimensional linearized theory of elastic waves in an initially stressed body. The main focus is on the influence of the mechanical properties of the constituent materials and the initial stresses present on the “resonance” values of the normal stress acting on the interface plane and on the “resonance” values of the frequency of the external point-located force. The numerical results are presented and discussed. In particular, it is shown that the values of the normal stress decrease with a decrease in the modulus of elasticity of the materials along the thickness of the covering layer.

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References

  1. Guz, A.N.: Elastic Waves in a Body with Initial Stresses. I. General Theory (in Russian). Naukova Dumka, Kiev (1986)

  2. Guz, A.N.: Elastic Waves in a Body with Initial Stresses. II. Propagation Laws (in Russian). Naukova Dumka, Kiev (1986)

  3. Guz, A.N.: Elastic Waves in Bodies with Initial (Residual) Stresses (in Russian). ASK, Kiev (2004)

  4. Akbarov S.D.: Recent investigations on the dynamical problems of the elastic body with initial (residual) stresses (review). Int. Appl. Mech. 43(12), 3–27 (2007)

    Article  MATH  Google Scholar 

  5. Guz A.N.: Elastic waves in bodies with initial (residual) stresses. Int. Appl. Mech. 38, 23–59 (2002)

    Article  MathSciNet  Google Scholar 

  6. Zhuk Yu.A., Guz I.A.: Feature of plane wave propagation along the layers of a pre-strained nanocomposites. Int. Appl. Mech. 43(4), 361–379 (2007)

    Article  Google Scholar 

  7. Akbarov S.D.: The influence of the third order elastic constants on the dynamical interface stress field in a half-space covered with a pre-strained layer. Int. J. Non-Linear Mech. 41, 417–425 (2006)

    Article  Google Scholar 

  8. Akbarov S.D.: Dynamical (time-harmonic) axisymmetric interface stress field in the finite pre-strained half-space covered with the finite pre-stretched layer. Int. J. Eng. Sci. 44, 93–112 (2006)

    Article  MathSciNet  Google Scholar 

  9. Akbarov S.D.: On the dynamical axisymmetric stress field in a finite pre-stretched bilayered slab resting on a rigid foundation. J. Sound Vib. 294, 221–237 (2006)

    Article  Google Scholar 

  10. Akbarov S.D.: Frequency response of the axisymmetrically finite pre-stretched slab from incompressible functionally graded material on a rigid foundation. Int. J. Eng. Sci. 44, 484–500 (2006)

    Article  MathSciNet  Google Scholar 

  11. Akbarov S.D.: The axisymmetric Lamb’s problem for the finite pre-strained half-space covered with the finite pre-stretched layer. Int. Appl. Mech. 43(3), 351–360 (2007)

    Article  Google Scholar 

  12. Akbarov S.D., Guler C.: Dynamical (harmonic) interface stress field in the half-plane covered by the pre-stretched layer under a strip load. J. Strain Anal. Eng. Des. 40(3), 225–236 (2005)

    Article  Google Scholar 

  13. Akbarov S.D., Guler C.: On the stress field in a half-plane covered by the pre-stretched layer under the action of arbitrary linearly located time-harmonic forces. Appl. Math. Model. 31, 2375–2390 (2007)

    Article  MATH  Google Scholar 

  14. Yahnioglu N.: On the stress distribution in the pre-strained simply supported strip containing two neighboring circular holes under forced vibration. Int. Appl. Mech. 43(10), 135–140 (2007)

    Article  MATH  Google Scholar 

  15. Lamb H.: On the propagation of tremors over the surface of an elastic solid. Philos. Trans. R. Soc. A203, 1–42 (1904)

    Google Scholar 

  16. Gladwell G.M.L.: The calculations of mechanical impedances related with the surface of semi-infinite elastic body. J. Sound Vib. 8, 215–219 (1968)

    Article  Google Scholar 

  17. Robertson I.A.: Forced vertical vibration of a rigid circular disc on a semi-infinite solid. Proc. Camb. Philos. Soc. 62, 547–557 (1966)

    Article  MATH  Google Scholar 

  18. Vasiliev, V.V., Protasov, V.D., Bolotin, V.V. (eds.): Handbook of Composite Materials (in Russian). Mashinostroenie, Moscow (1990)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, Besiktas, 34349, Istanbul, Turkey

    Surkay Akbarov

  2. Institute of Mathematics and Mechanics, The National Academy of Sciences of Azerbaijan, 370141, Baku, Azerbaijan

    Surkay Akbarov

  3. Department of Civil Engineering, Faculty of Civil Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34220, Istanbul, Turkey

    Nihat İlhan

Authors
  1. Surkay Akbarov
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  2. Nihat İlhan
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Correspondence to Nihat İlhan.

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Akbarov, S., İlhan, N. Time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane. Arch Appl Mech 80, 1271–1286 (2010). https://doi.org/10.1007/s00419-009-0369-z

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  • DOI: https://doi.org/10.1007/s00419-009-0369-z

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