Mechanics of Composite Materials

, Volume 55, Issue 1, pp 85–94 | Cite as

Resolving Controls for the Boundary Approximate Controllability of Sandwich Beams with Uncertainties the Green’s Function Approach

  • As. Zh. KhurshudyanEmail author
  • Sh. Kh. Arakelyan

The boundary approximate null-controllability of an Euler–Bernoulli sandwich beam subjected to a dynamically active distributed load is considered. The exact area and location of the distributed load are uncertain. The problem consists in controlling the vertical displacement at the beam end with the aim to damp its vibrations in a given a time. Using the recently developed Green’s function approach, the set of resolving controls is partially constructed. The results obtained are verified by numerical examples.


Euler–Bernoulli beam uncertainty Green’s function approach dynamic load bending nullcontrollability 


  1. 1.
    J.-M. Berthelot, Composite Materials: Mechanical Behavior and Structural Analysis, Springer, Berlin (1999).CrossRefGoogle Scholar
  2. 2.
    S. V. Sarkisyan, S. H. Jilavyan, and As. Zh. Khurshudyan, “Structural optimization of an inhomogeneous infinite layer in problems on propagation of periodic waves,” Mech. Compos. Mater., 51, No. 3, 277-284 (2015).CrossRefGoogle Scholar
  3. 3.
    G. Wrobel, M. Szymiczek, and J. Kaczmarczyk, “Influence of the structure and number of reinforcement layers on the stress state in the shells of tanks and pressure pipes,” Mech. Compos. Mater., 53, No 2, 165-178 (2017).CrossRefGoogle Scholar
  4. 4.
    P. Priyanka, A. Dixit, and H. S. Mali, “High-strength hybrid textile composites with carbon, kevlar, and E-glass fibers for impact-resistant structures. A Review,” Mech. Compos. Mater., 53, No. 5, 685-704 (2017).CrossRefGoogle Scholar
  5. 5.
    S. Tekili, Y. Khadri, B. Merzoug, E. M. Daya, and A. Daouadji, “Free and forced vibration of beams strengthened by composite coats subjected to moving loads,” Mech. Compos. Mater., 52, No. 6, 789-798 (2016).CrossRefGoogle Scholar
  6. 6.
    A. Muc, “Optimization of multilayered composite structures with randomly distributed mechanical properties,” Mech. Compos. Mater., 41, No. 6, 505-510 (2005).CrossRefGoogle Scholar
  7. 7.
    A. Muc, “Choice of design variables in the stacking sequence optimization for laminated structures”, Mech. Comp. Mat., 52, no. 2, 211-224 (2016).CrossRefGoogle Scholar
  8. 8.
    L. E. T. Ferreira, J. B. de Hanai, and V. J. Ferrari, “Optimization of a hybrid-fiber-reinforced high-strength concrete,” Mech. Compos. Mater., 52, No. 3, 295-304 (2016).CrossRefGoogle Scholar
  9. 9.
    A. Morka, P. Kedzierski, and P. Muzolf, “Optimization of the structure of a ceramic-aluminum alloy composite subjected to the impact of hard steel projectiles,” Mech. Compos. Mater., 52, No. 3, 333-346 (2016).CrossRefGoogle Scholar
  10. 10.
    E. M. Nurullaev and A. S. Ermilov, “Optimizing the composition of elastomer composites for the fracture energy,” Mech. Compos. Mater., 52, No. 2, 225-230 (2016).CrossRefGoogle Scholar
  11. 11.
    T. A. Galichyan and As. Zh. Khurshudyan, “Parameter optimization for laminated multiferroic composites”, In “Problems of Mechanics of a Deformable Solid Body”, dedicated to the 95th anniversary of Academician of NAS of Armenia, Sergey A. Ambartsumyan. Institute of Mechanics, NAS of Armenia, 159-166 (2017).Google Scholar
  12. 12.
    J. Li and Y. Narita, “Vibration suppression for laminated composite plates with arbitrary boundary conditions,” Mech. Compos. Mater., 49, No. 5, 519-530 (2013).CrossRefGoogle Scholar
  13. 13.
    S. Adali, J. C. Bruch Jr., I. S. Sadek, and J. M. Sloss, “Transient vibrations of cross-ply plates subject to uncertain excitations,” Appl. Math. Modeling, 19, No. 1, 56-63 (1995).CrossRefGoogle Scholar
  14. 14.
    I. Elishakoff and M. Ohsaki, Optimization and Antioptimization of Structures under Uncertainty, Imperial College Press, London (2010).CrossRefGoogle Scholar
  15. 15.
    I. S. Radebe and S. Adali, “Minimum weight design of beams against failure under uncertain loading by convex analysis,” J. Mech. Sci. & Tech., 27, No. 7, 2071-2078 (2013).CrossRefGoogle Scholar
  16. 16.
    A. S. Avetisyan and As. Zh. Khurshudyan, Controllability of Dynamic Systems: The Green’s Function Approach, Cambridge Scholars Publishing, Cambridge (2018).Google Scholar
  17. 17.
    A. D. Polyanin and V. E. Nazaikinskii, Handbook of Linear Partial Differential Equations for Engineers and Scientists. 2nd ed. Chapman & Hall/CRC Press, Boca Raton (2016).CrossRefGoogle Scholar
  18. 18.
    P. P. Teodorescu, W. W. Kecs, and A. Toma, Distribution Theory: With Applications in Engineering and Physics, WILEY-VCH Verlag, Weinheim (2003).Google Scholar
  19. 19.
    A. S. Avetisyan and As. Zh. Khurshudyan, “Green’s function approach in approximate controllability problems,” Proc. NAS Arm. Mech., 69, No. 2, 3-20 (2016).Google Scholar
  20. 20.
    A. S. Avetisyan and As. Zh. Khurshudyan, “Green’s function approach in approximate controllability for nonlinear physical processes,” Mod. Phys. Let. A, 32, No. 21, 1730015 (2017).CrossRefGoogle Scholar
  21. 21.
    As. Zh. Khurshudyan, “Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems,” Math. Probl. Engineer., Article ID 9496371, 16 p.Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of ArmeniaYerevanArmenia
  2. 2.Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiP.R. China
  3. 3.Faculty of RadiophysicsYerevanArmenia

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