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Determination of Damping Properties of an Elongated Plate with an Integral Damping Coating on the Base of Studying Complex Eigenfrequencies

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Abstract

We describe the structure of a perspective integral damping coating consisting (with respect to the thickness) of two layers of a viscoelastic material with a thin reinforcing layer in-between. We propose a four-layer finite element model with fourteen degrees of freedom for a plate with a mentioned damping coating. This model allows us to take into account the effect of transversal compression of damping layers under high-frequency vibrations of the plate. For determining some lower complex modes and frequencies of free vibrations of the damped plate, we solve a generalized complex eigenvalue problem using the method of iterations in a subspace.

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References

  1. Chernyshev, V.M. Vibration Damping of Mechanical Systems by Means of Polymeric Coatings (Nauka, Moscow, 2004) [in Russian].

    Google Scholar 

  2. Kerwin, E. “Damping of Flexural Waves by a Constrained Viscoelastic Layer”, J. Acoustical Soc. America 3 (7), 952–962 (1959).

    Article  Google Scholar 

  3. Ungar, E. “Loss Factors of Viscoelastically Damped Beam Structures”, J. Acoustical Soc. America 34 (8), 1082–1089 (1962).

    Article  Google Scholar 

  4. Amadori, S., Catania, G. “Damping Contributions of Coatings to the Viscoelastic Behavior of Mechanical Components” (in: Proc. of the Inter. Conf. Surveillance 9, Fes. Morocco, 22–24 May 2017).s

  5. Fisher, D.K., Asthana, S. Self-Adhesive Vibration Damping Tape and Composition, Patent US 6828020 B2, 7.12.2004.

  6. Pan’kov, L.A., Fesina, M.I., Krasnov, A.V. Vibration Damping Flat Sheet, Patent RF no. 2333545, 10.09.2008.

  7. Tesse, S., Stopin, G. Constrained-Layer Damping Material, Patent EP2474971A1, 11.07.2012.

  8. Nashif, A.D., Jones, D.I.G., Henderson, J.P. Vibration Damping (Wiley Interscience, New York, 1985; Mir, Moscow, 1988).

    Google Scholar 

  9. Rikards, R.B., Barkanov, E.N. “Determination of the Dynamic Characteristics of Vibration-Absorbing Coatings by the Finite-Element Method”, Mechanics of Composite Materials 5, 823–830 (1991).

    Google Scholar 

  10. Postnikov, V.S. Internal Friction in Metals (Metallurgiya, Moscow, 1969) [in Russian].

    Google Scholar 

  11. Khil’chevskii, V.V., Dubenets, V.G. Energy Dissipation during Vibrations of Thin-Wall Elements of Constructions (Vishcha Shkola, Kiev, 1977) [in Russian].

    Google Scholar 

  12. Sorokin, E.S. To the Theory of Internal Friction under Vibrations of Elastic Systems (Gosstroiizdat, Moscow, 1960) [in Russian].

    Google Scholar 

  13. Paimushin, V.N., Firsov, V.A., Gyunal, I., Shishkin, V.M. “Identification of the Elastic and Damping Characteristics of Soft Materials Based on the Analysis of Damped Flexural Vibrations of Test Specimens”, Mechan. of Composite Mater. 52 (4), 435–454 (2016).

    Article  Google Scholar 

  14. Norrie, D.H. de Vries, G. The Finite Element Method (Academic Press, New York, 1973; Mir, Moscow, 1981).

    MATH  Google Scholar 

  15. Segerlind, L.D. Applied Finite Element Analysis (John Wiley and Sons, Inc., New York, 1976; Mir, Moscow, 1979).

    MATH  Google Scholar 

  16. Zenkevich, O. Finite Element Method in Engineering Science (John Wiley and Sons, Inc., New York, 1971; Mir, Moscow, 1975).

    Google Scholar 

  17. Demidovich, B.P., Maron, I.A. Computational Mathematics (Mir, Moscow, 1966).

    MATH  Google Scholar 

  18. Matthews J.H., Fink, K.D. Numerical Methods Using MATLAB (3rd Edition) (Prentice-Hall, New York, 1998; Vil’yams, Moscow, 2001).

    Google Scholar 

  19. Johnson, C.D., Kienholz, D.A. “Finite Element Prediction of Damping in Structures with Constrained Viscoelastic Layers”, Aerokosmicheskaya Tekhn. 1 (4), 124–133 (1983).

    Google Scholar 

  20. Bathe, K.-J., Wilson, E.L. Numerical Methods in Finite Element Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1976; Stroiizdat, Moscow, 1982).

    MATH  Google Scholar 

  21. Clough, R.W., Penzien, J. Dynamics of Structures (McGraw-Hill, 1982; Stroiizdat, Moscow, 1979).

  22. Parlett, B.N. The Symmetric Eigenvalue Problem. Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1980; Mir, Moscow, 1983).

    MATH  Google Scholar 

  23. Paimushin, V.N., Shishkin, V.M. “Modeling the Elastic and Damping Properties of the Multilayered Torsion Bar-Blade Structure of Rotors of Light Helicopters of the New Generation. 1. Finite-Element Approximation of the Torsion Bar”, Mechan. Composite Mater. 51 (5), 609–628 (2015).

    Article  Google Scholar 

  24. Pisarenko, G.S., Yakovlev, A.P., Matveev, V.V. Vibration-Absorbing Properties of Structural Materials Handbook (Naukova Dumka, Kiev, 1971) [in Russian].

    Google Scholar 

  25. Caughey, T.K., O’Kelly, M.E.J. “Effect of Damping on the Natural Frequencies of Linear Dynamic Systems”, J. Acoustical Soc. America. 33 (11), 1458–1461 (1961).

    Article  MathSciNet  Google Scholar 

  26. Barkanov, E.N. “Method of Complex Eigenvalues for Studying the Damping Properties of Sandwich-Type Structures”, Mechanics of Composite Materials 29 (1), 116–121 (1993).

    Article  Google Scholar 

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Funding

This work was supported by the Russian Scientific Foundation (project no. 19-19-00058).

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Authors and Affiliations

  1. Kazan National Research Technical University, 10 K. Marks str., Kazan, 420111, Russia

    V. N. Paimushin & V. A. Firsov

  2. Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008, Russia

    V. N. Paimushin

  3. Vyatka State University, 36 Moskovskaya str., Kirov, 610000, Russia

    V. M. Shishkin

Authors
  1. V. N. Paimushin
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  2. V. A. Firsov
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  3. V. M. Shishkin
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Corresponding authors

Correspondence to V. N. Paimushin, V. A. Firsov or V. M. Shishkin.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 6, pp. 48–64.

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Paimushin, V.N., Firsov, V.A. & Shishkin, V.M. Determination of Damping Properties of an Elongated Plate with an Integral Damping Coating on the Base of Studying Complex Eigenfrequencies. Russ Math. 64, 40–55 (2020). https://doi.org/10.3103/S1066369X20060079

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  • DOI: https://doi.org/10.3103/S1066369X20060079

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