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Exponential Stability of Laminated Beams with Interfacial Slip

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Abstract—

We study the stability of a one-dimensional laminated beam which consists of two identical layers of uniform thickness. An adhesive of small thickness is bonding the two layers and creating a restoring force thereby producing a damping called adhesive or structural damping at the interface. It is well-known in the literature that this single frictional damping is not strong enough to stabilize the system exponentially. On the contrary, we prove in this paper that the unique dissipation due to the structural damping is strong enough to exponentially stabilize the system provided the wave speeds of the system are equal.

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REFERENCES

  1. S. W. Hansen and R. D. Spies, “Structural damping in laminated beams due to interfacial slip,” J. Sound Vib. 204 (2), 183–202 (1997).

    Article  ADS  Google Scholar 

  2. T. A. Apalara, “Uniform stability of a laminated beam with structural damping and second sound,” Z. Angew. Math. Phys. 68 (2), 41 (2017).

    Article  MathSciNet  Google Scholar 

  3. C. A. Raposo, “Exponential stability for a structure with interfacial slip and frictional damping,” Appl. Math. Lett. 53, 85–91 (2016).

    Article  MathSciNet  Google Scholar 

  4. J. M. Wang, G. Q. Xu, and S. P. Yung, “Exponential stabilization of laminated beams with structural damping and boundary feedback controls,” SIAM J. Control Optim. 44 (5), 1575–1597 (2005).

    Article  MathSciNet  Google Scholar 

  5. A. Lo and N. E. Tatar, “Exponential stabilization of a structure with interfacial slip,” Discr. Contin. Dyn. Syst.-A 36 (11), 6285–6306 (2016).

  6. A. Lo and N. E. Tatar, “Stabilization of laminated beams with interfacial slip,” Electr. J. Diff. Equat. 2015 (129), 1–14, (2015).

    Article  MathSciNet  Google Scholar 

  7. X. G. Cao, D. Y. Liu, and G. Q. Xu, “Easy test for stability of laminated beams with structural damping and boundary feedback controls,” J. Dyn. Control Syst. 13 (3), 313–336 (2007).

    Article  MathSciNet  Google Scholar 

  8. B. Feng, “Well-posedness and exponential decay for laminated Timoshenko beams with time delays and boundary feedbacks,” Math. Meth. Appl. Sci. 41 (3), 1162–1174 (2018).

    Article  MathSciNet  Google Scholar 

  9. A. Lo and N. E. Tatar, “Uniform stability of a laminated beam with structural memory,” Qual. Theory Dyn. Syst. 15 (2), 517–540 (2016).

    Article  MathSciNet  Google Scholar 

  10. M. I. Mustafa, “Boundary control of laminated beams with interfacial slip,” J. Math. Phys. 59 (5), 051508 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  11. M. I. Mustafa, “On the stabilization of viscoelastic laminated beams with interfacial slip,” Z. Angew. Math. Phys. 69 (2), 33 (2018).

    Article  MathSciNet  Google Scholar 

  12. M. I. Mustafa, “Laminated Timoshenko beams with viscoelastic damping,” J. Math. Anal. Appl. 466 (1), 619–641 (2018).

    Article  MathSciNet  Google Scholar 

  13. N. -E. Tatar, “Stabilization of a laminated beam with interfacial slip by boundary controls,” Bound. Value Probl. 2015 (1), 169 (2015).

    Article  MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

The author thanks UHB for its continuous support.

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Authors and Affiliations

  1. University of Hafr Al-Batin, 31991, Mathematics Department Hafr Al-Batin, Saudi Arabia

    Tijani A. Apalara

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  1. Tijani A. Apalara
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Correspondence to Tijani A. Apalara.

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Apalara, T.A. Exponential Stability of Laminated Beams with Interfacial Slip. Mech. Solids 56, 131–137 (2021). https://doi.org/10.3103/S0025654421010039

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  • DOI: https://doi.org/10.3103/S0025654421010039

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