Skip to main content

Advertisement

Log in

Analytical modeling and damping optimization for a thin plate partially covered with hard coating

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Finding the best coating location with the fixed shape of the hard coating is an urgent need for the engineering application of the hard-coating damping. In this paper, a study on optimal placement of hard-coating damping treatment for vibration reduction in the cantilever plate was presented. Based on the energy method and the assumed mode method, the analytical model was derived for free vibration analysis of the thin plate partially covered with hard coating, and the modal loss factors of the coating structure were determined by the modified modal strain energy method. The damping optimization model of the hard-coating thin plate was described with the maximum modal loss factor of single order or multi-orders as the objective function and the coating position as the design variable. Moreover, a method named multiple population genetic algorithms was proposed to search for the optimal coating position. Finally, a cantilever titanium plate with a single side partially deposited with NiCrAlCoY+YSZ hard coating was taken as an example to carry out a case study. The correctness of the analytical results was verified by ANSYS software and experiment, and the rationality of the damping optimization results for the hard-coating plate was also verified by experiment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Ivancic, F., Palazotto, A.: Experimental considerations for determining the damping coefficients of hard coatings. J. Aerosp. Eng. 18(1), 8–17 (2005)

    Article  Google Scholar 

  2. Blackwell, C., Palazotto, A., George, T.J., et al.: The evaluation of the damping characteristics of a hard coating on titanium. Shock Vib. 14(1), 37–51 (2007)

    Article  Google Scholar 

  3. Du, G.Y., Ba, D.C., Tan, Z., et al.: Vibration damping performance of ZrTiN coating deposited by arc ion plating on TC4 Titanium alloy. Surf. Coat. Technol. 229, 172–175 (2013)

    Article  Google Scholar 

  4. Patsias, S., Saxton, C., Shipton, M.: Hard damping coatings: an experimental procedure for extraction of damping characteristics and modulus of elasticity. Mater. Sci. Eng. A 370(1), 412–416 (2004)

    Article  Google Scholar 

  5. Filippi, S., Torvik, P.J.: A methodology for predicting the response of blades with nonlinear coatings. J. Eng. Gas Turbines Power 133(4), 042503 (2011)

    Article  Google Scholar 

  6. Bruce, R.W., Schell, J.D.: Process for depositing a coating on a blisk. U.S. Patent Application 12/241,678, 2008-9-30

  7. Green, J., Patsias, S.: A preliminary approach for the modeling of a hard damping coating using friction elements. In: Proceedings of the Seventh National Turbine Engine High Cycle Fatigue Conference. 2002,7c1-7c9 (2002)

  8. Reed, S.A.: Development of Experimental, Analytical, and Numerical Approximations Appropriate for Nonlinear Damping Coatings. Air Force Institute of Technology, Wright-Patterson AFB (2007)

    Google Scholar 

  9. Yang, Z.X., Han, Q.K., Jin, Z.H., et al.: Solution of natural characteristics of a hard-coating plate based on Lindstedt-Poincaré perturbation method and its valedictions by FEM and measurement. Nonlinear Dyn. 81(3), 1207–1218 (2015)

    Article  MATH  Google Scholar 

  10. Li, H., Ying, L., Sun, W.: Analysis of nonlinear vibration of hard coating thin plate by finite element iteration method. Shock Vib. (2014). https://doi.org/10.1155/2014/941709

  11. Chen, Y., Zhai, J., Han, Q.: Vibration and damping analysis of the bladed disk with damping hard coating on blades. Aerosp. Sci. Technol. 58, 248–257 (2016)

    Article  Google Scholar 

  12. Sun, W., Liu, Y.: Vibration analysis of hard-coated composite beam considering the strain dependent characteristic of coating material. Acta. Mech. Sin. 32(4), 731–742 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sun, W., Liu, Y., Du, G.: Analytical modeling of hard-coating cantilever composite plate considering the material nonlinearity of hard coating. Math. Probl. Eng. (2015). https://doi.org/10.1155/2015/978392

  14. Sun, W., Zhu, M., Wang, Z.: Free vibration analysis of a hard-coating cantilever cylindrical shell with elastic constraints. Aerosp. Sci. Technol. 63, 232–244 (2017)

    Article  Google Scholar 

  15. Sun, W., Han, Q., Qi, F.: Optimal design of damping capacity for hard-coating thin plate. Adv. Vib. Eng. 12(2), 179–192 (2013)

    Google Scholar 

  16. Sun, W., Liu, R.: Damping optimization of hard-coating thin plate by the modified modal strain energy method. Coatings 7(2), 32 (2017)

    Article  Google Scholar 

  17. Lumsdaine, A., Scott, R.A.: Shape optimization of unconstrained viscoelastic layers using continuum finite elements. J. Sound Vib. 216(1), 29–52 (1998)

    Article  Google Scholar 

  18. Lumsdaine, A.: Topology optimization of constrained damping layer treatments. In: ASME 2002 International Mechanical Engineering Congress and Exposition. pp. 149–156 (2002)

  19. Lumsdaine, A., Pai, R.: Design of constrained layer damping topologies. In: ASME 2003 International Mechanical Engineering Congress and Exposition. pp. 219–227 (2003)

  20. Chen, Y.C., Huang, S.C.: An optimal placement of CLD treatment for vibration suppression of plates. Int. J. Mech. Sci. 44(8), 1801–1821 (2002)

    Article  MATH  Google Scholar 

  21. Damu, M., Lumsdaine, A.: Determination of optimal orientations and volume fractions of nanotubes in a polymer for vibration damping. In: ASME 2006 International Mechanical Engineering Congress and Exposition, pp. 139–143 (2006)

  22. Hou, S.W., Jiao, Y.H., Chen, Z.B.: Optimum layout of passive constrained layer damping treatment using genetic algorithms. In: ASME 2010 International Mechanical Engineering Congress and Exposition. pp. 371–376 (2010)

  23. Araújo, A.L., Soares, C.M.M., Soares, C.A.M., et al.: Optimal design and parameter estimation of frequency dependent viscoelastic laminated sandwich composite plates. Compos. Struct. 92(9), 2321–2327 (2010)

    Article  Google Scholar 

  24. Zheng, H., Cai, C., Pau, G.S.H., et al.: Minimizing vibration response of cylindrical shells through layout optimization of passive constrained layer damping treatments. J. Sound Vib. 279(3), 739–756 (2005)

    Article  Google Scholar 

  25. Patsias, S., Tassini, N., Lambrinou, K.: Ceramic coatings: effect of deposition method on damping and modulus of elasticity for yttria-stabilized zirconia. Mater. Sci. Eng. A 442(1), 504–508 (2006)

    Article  Google Scholar 

  26. Maurini, C., Pouget, J., Dell’Isola, F.: On a model of layered piezoelectric beams including transverse stress effect. Int. J. Solids Struct. 41(16), 4473–4502 (2004)

    Article  MATH  Google Scholar 

  27. Maurini, C., Pouget, J., Dell’Isola, F.: Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach. Comput. Struct. 84(22), 1438–1458 (2006)

    Article  Google Scholar 

  28. Mahi, A., Tounsi, A.: A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Appl. Math. Model. 39(9), 2489–2508 (2015)

    Article  MathSciNet  Google Scholar 

  29. Hwang, S.J., Gibson, R.F.: The use of strain energy-based finite element techniques in the analysis of various aspects of damping of composite materials and structures. J. Compos. Mater. 26(17), 2585–2605 (1992)

    Article  Google Scholar 

  30. Potts, J.C., Giddens, T.D., Yadav, S.B.: The development and evaluation of an improved genetic algorithm based on migration and artificial selection. IEEE Trans. Syst. Man Cybern. 24(1), 73–86 (1994)

    Article  Google Scholar 

Download references

Acknowledgements

This project was supported by National Natural Science Foundation of China (Grant No. 51375079).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wei Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, W., Liu, R. & Fan, Y. Analytical modeling and damping optimization for a thin plate partially covered with hard coating. Arch Appl Mech 88, 897–912 (2018). https://doi.org/10.1007/s00419-018-1348-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1348-z

Keywords

Navigation