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Numerical Modeling of Resonant Vibrations of an Elongate Plate with an Integral Damping Coating

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Mechanics of Composite Materials Aims and scope

The classical methods of surface damping of bending vibrations of thin-walled structures and a promising integrated version with a damping coating consisting of two layers of a material with pronounced viscoelastic properties and an intermediate thin reinforcing layer of a high-modulus material are discussed. A four-layer finite element for an elongate plate with an integral damping coating is developed taking into account the lateral compression of the damping layers. A system of governing equations of the finite-element method is constructed for analyzing the dynamic response of the plate during its resonant vibrations. Iterative algorithms have been developed to take into account the amplitude dependence of the logarithmic decrements of vibrations of material of the damping layers when determining the damping properties of the plate and determining its vibration eigenmodes and eigenfrequencies with consideration of frequency dependence of the dynamic elastic moduli of the material. Numerical experiments were carried out to test the finite element developed and the iterative algorithms mentioned. The influence of aerodynamic resistance forces on the overall damping level of a cantilever plate with an integral damping coating is assessed.

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References

  1. G. S. Pisarenko, A. P. Yakovlev, and V. V. Matveev, “Vibroabsorption Properties of Structural Materials. A Handbook [in Russian], Kiev, Naukova Dumka (1971).

    Google Scholar 

  2. V. S. Postnikov, Internal Friction in Metals [in Russian], M., Metallurgia (1969).

  3. V. M. Chernyshev, Damping the Vibrations of Mechanical Systems by Coverings of Polymer Materials [in Russian], M., Nauka (2004).

  4. E. Kerwin, “Damping of flexural waves by a constrained viscoelastic layer,” J. Acoustical Soc. Am., 3, No. 7, 952-962 (1959).

    Article  Google Scholar 

  5. E. Ungar, “Loss coefficients of viscoelastically damped beam structures,” J. Acoustical Soc. Am. 34, No. 8, 1082-1089 (1962).

    Article  Google Scholar 

  6. А. Nashif, D. Jouns, and J. Henderson, Damping of Vibrations [Russian translation], M., Mir (1988).

  7. ASTM E756-05: Standard test method for measuring vibration-damping properties of materials, ASTM Int., PA, (2010).

  8. D. K. Fisher and S. Asthana, “Self-adhesive vibration damping tape and composition.” Patent US 6828020 B2, 7.12.2004.

  9. L. A. Pankov, M. I. Fesina, and A. V. Krasnov, “Vibroshumodempfirujushchaja плосколистовая a lining.” Patent of the Russian Federation № 2333545, 10.09.2008.

  10. C. Tesse, and G. Stopin, “Constrained-layer damping material.” Patent EP2474971A1, 11.07.2012.

  11. R. B. Rikards and E. N. Barkanov, “Determination of the dynamic characteristics of vibration-absorbing coating by the finite element method,” Mech. Compos. Mater., 27, No. 5, 529-534 (1991).

    Article  Google Scholar 

  12. E. N. Barkanov, “Method of complex eigenvalues for studying the damping properties of sandwich-type structures,” Mech. Compos. Mater., 29, No. 1, 90-94 (1993).

    Article  Google Scholar 

  13. V. Oravsky, S. Markus, and O. Simkova, “A new approximate method of finding the loss-coefficients of a sandwich cantilever,” J. Sound Vibration, 33, No. 3, 335-352 (1974).

    Article  Google Scholar 

  14. D. J. Mead and S. Markus, “The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary states,” J. Sound Vibration, 10, No. 2, 165-175 (1969).

    Article  Google Scholar 

  15. D. K. Rao, “Vibration of short sandwich beams,” J. Sound Vibration, 52, No. 2, 253-263 (1977).

    Article  Google Scholar 

  16. M. Amabili, “Nonlinear damping in nonlinear vibrations of rectangular plates: Derivation from viscoelasticity and experimental validation,” J. Mech. and Physics of Solids, 118, 275-292 (2018).

    Article  Google Scholar 

  17. V. N. Paimushin, V. A. Firsov, I. Gyunal, and V. M. Shishkin, “Considering the vibration dependence of the dynamic elastic modulus of Duralumin in deformation problems,” Prikl. Mekh. Tekhn. Fiz., 58, No. 3, 163-177 (2017).

    Google Scholar 

  18. V. N. Paimushin, V. A. Firsov, I. Gyunal, and V. M. Shishkin, “Identification of the elastic characteristics of soft materials based on the analysis of damped flexural vibrations of test specimens,” Mech. Compos. Mater., 52, No. 4, 615-644 (2016).

    Article  Google Scholar 

  19. V. N. Paimushin, V. A. Firsov, and V. M. Shishkin, “Identifying the dynamic characteristics of elasticity and damping properties of an OT-titanium alloy on the basis of research of damped flexural vibrations of tests specimens,” Probl. Mashinostr. Nadezhn. Mashin, No. 2, 27-39 (2019).

  20. V. N. Paimushin, V. A. Firsov, and V. M. Shishkin, “Modeling the response of a carbon-fiber-reinforced plate at resonant vibrations considering the internal friction in the material and the external aerodynamic damping,” Mech. Compos. Mater., 53, No. 4, 609-630 (2017).

    Article  Google Scholar 

  21. Ya. G. Panovko, Internal Friction in Vibrations of Elastic Systems [in Russian], M., Fizmatgiz (1960).

  22. V. V. Khil’chevskii and V. G. Dubenec, Energy Dissipation in Vibrations of Thin-Walled Structural Elements [in Russian], Kiev, Vishcha Shkola (1977).

    Google Scholar 

  23. O. Zenkevich, Finite-Elements Method in Engineering [Russian translation], M., Mir (1975).

  24. L. Segerlind, Employment of the Finite-Element Method [Russian translation], M., Mir (1979).

  25. К. Bath and E. Wilson, Numerical Methods of Analysis and the Finite-Element Method [Russian translation], M., Stroyizdat (1982).

  26. T. Shup, Solution of Engineering Problems on a Computer [Russian translation], M., Mir (1982).

  27. V. N. Paimushin, V. A. Firsov, I. Gunal, and V. M. Shishkin, “Theoretical-experimental method for evaluating the elastic and damping characteristics of soft materials based on studying the resonant flexural vibrations of test specimens,” Mech. Compos. Mater., 52, No. 5, 813-830 (2016).

    Article  Google Scholar 

  28. B. Parlett, Symmetric Problem of Eigenvalues. Numerical Methods [Russian translation], M., Mir (1983).

  29. J. G. Methus and D. Fink Kurtis, Numerial Methods. Use MATLAB [Russian translation], M., Izd. Dom “Williams,” (2001).

  30. Yu. P. Boglaev, Computation Mathematics and Programming, M., Vysshaya Shkola, (1990).

  31. Р. Klaf and J. Penzien, Dynamics of Constructions [Russian translation], M., Stroiizdat. (1979).

  32. V. N. Paimushin, V. A. Firsov, I. Gyunal, and A. G. Egorov, “Theoretical-experimental method for determining the parameters of damping based on the study on damped flexural vibrations of test specimens. 1. Experimental basis,” Mech. Compos. Mater., 50, No. 2, 185-198 (2014).

    Article  Google Scholar 

  33. A. G. Egorov, A. M. Kamalutdinov, V. N. Paimushin, and V. A. Firsov, “Theoretical-experimental method for determining the coefficient of aerodynamic resistance of a harmonically vibrating thin plate,” Prikl. Mekh. Tekhn. Fiz., 57, No. 2, 96-104 (2016).

    Google Scholar 

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Authors and Affiliations

  1. A. N. Tupolev, Kazan National Research Technical University, Kazan, Russia

    V. N. Paimushin & V. A. Firsov

  2. Kazan (Volga Region) Federal University, Kazan, Russia

    V. N. Paimushin & V. M. Shishkin

  3. Vyatka State University, Kirov, Russia

    V. N. Paimushin, V. A. Firsov & 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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Correspondence to V. N. Paimushin.

Additional information

Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 2, pp. 225-252, March-April, 2020.

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Paimushin, V.N., Firsov, V.A. & Shishkin, V.M. Numerical Modeling of Resonant Vibrations of an Elongate Plate with an Integral Damping Coating. Mech Compos Mater 56, 149–168 (2020). https://doi.org/10.1007/s11029-020-09869-3

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  • DOI: https://doi.org/10.1007/s11029-020-09869-3

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