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Nonlinear harmonic response characteristics and experimental investigation of cantilever hard-coating plate

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Abstract

The nonlinear harmonic response of a cantilever hard-coating plate which is made of a layer of anisotropic hard-coating material and isotropic metal substrate is investigated based on the theory of high-order shear deformation of plate. Firstly, based on the theories of von Karman and Reddy’s three-order shear deformation, the nonlinear dynamic equations of hard-coating plate are built by Hamilton variation principle. Secondly, to obtain nonlinear governing equation of hard-coating plate under transverse load, these equations are discretized in Galerkin method. The system averaged equations with 1:3 internal resonances are obtained by the method of multiple scales, and the multi-periodic responses behavior of cantilever hard-coating plate under transverse loading could be presented. Finally, the vibration response experiment of hard-coating plate is conducted, and the multi-periodic responses are also present for the hard-coating plate with three-to-one internal resonance. Besides, through the vibration response experiment of uncoated titanium alloy plate, the damping characteristic of hard coating is further analyzed.

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References

  1. Han, M., Zhou, G.D., Huang, J.H., Chen, S.H.: A parametric study of the double-ceramic-layer thermal barrier coatings part I: optimization design of the ceramic layer thickness ratio based on the finite element analysis of thermal insulation. Surf. Coat. Technol. 236(3), 500–509 (2013)

    Article  Google Scholar 

  2. Torvik, P.J.: Determination of mechanical properties of non-linear coatings from measurements with coated beams. Int. J. Solids Struct. 46(5), 1066–1077 (2009)

    Article  MATH  Google Scholar 

  3. Al-Rub, R.K.A., Palazotto, A.N.: Micromechanical theoretical and computational modeling of energy dissipation due to nonlinear vibration of hard ceramic coatings with microstructural recursive faults. Int. J. Solids Struct. 47(16), 2131–2142 (2010)

    Article  MATH  Google Scholar 

  4. Tassini, N., Patsias, S., Lambrinou, K.: Ceramic coatings: a phenomenological modeling for damping behavior related to microstructural features. Mater. Sci. Eng. A 442(1–2), 509–513 (2006)

    Article  Google Scholar 

  5. Chia, C.Y.: Nonlinear Analysis of Plates. Mc Graw-Hill, New York (1980)

    Google Scholar 

  6. Bhimaraddi, A., Stevens, L.: A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates. ASME J. Appl. Mech. 51(1), 195–198 (1984)

    Article  Google Scholar 

  7. Oh, K., Nayfeh, A.H.: High- to low-frequency modal interactions in a cantilever composite plate. J. Vib. Acoust. 120(2), 579–587 (1998)

    Article  Google Scholar 

  8. Reddy, J.N.: A simple higher-order theory for laminated composite plates. ASME J. Appl. Mech. 51, 745–752 (1984)

    Article  MATH  Google Scholar 

  9. Reddy, J.N., Phan, N.D.: Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory. J. Sound Vib. 98(2), 157–170 (1985)

    Article  MATH  Google Scholar 

  10. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., et al.: Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. Part B Eng. 44(1), 657–674 (2013)

    Article  Google Scholar 

  11. Khante, S.N., Rode, V.: Nonlinear dynamic bending analysis of plates using a higher-order shear deformation theory. Nonlinear Dyn. 43(3), 257–275 (2006)

    Article  MATH  Google Scholar 

  12. Khante, S.N., Rode, V., Kant, T.: Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory. Nonlinear Dyn. 47, 389–403 (2007)

    Article  MATH  Google Scholar 

  13. Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley-VCH, Brikach (2004)

    MATH  Google Scholar 

  14. Emam, S.A., Nayfeh, A.H.: Non-linear response of buckled beams to 1:1 and 3:1 internal resonances. Int. J. Non-Linear Mech. 52(6), 12–25 (2013)

    Article  Google Scholar 

  15. Kim, C.H., Perkins, N.C., Lee, C.W.: Parametric resonance of plates in a sheet metal coating process. J. Sound Vib. 268(4), 679–697 (2003)

    Article  Google Scholar 

  16. Wang, Z.X., Xu, J.F., Qiao, P.Z.: Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates. Compos. Struct. 108(1), 423–434 (2014)

    Google Scholar 

  17. Abe, A., Kobayashi, Y., Yamada, G.: Analysis of subharmonic resonance of moderately thick antisymmetric angle-ply laminated plates by using method of multiple scales. J. Sound Vib. 217(3), 467–484 (1992)

    Article  Google Scholar 

  18. Cacan, M.R., Leadenham, S., Leamy, M.J.: An enriched multiple scales method for harmonically forced nonlinear systems. Nonlinear Dyn. 78(2), 1205–1220 (2014)

    Article  MathSciNet  Google Scholar 

  19. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  20. Yamaki, N., Chiba, M.: Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement-part I: theory. Thin-Walled Struct. 1(1), 3–29 (1983)

  21. Yamaki, N., Otomo, K., Chiba, M.: Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement-part II: experiment. Thin-Walled Struct. 1(1), 101–119 (1983)

    Article  MATH  Google Scholar 

  22. Cole, S.R.: Effects of spoiler surfaces on the aeroelastic behavior of a low-aspect-ratio rectangular wing. J. Aircr. 29(5), 768–773 (1990)

    Article  Google Scholar 

  23. Oh, K.: A theoretical and experimental study of modal interactions in metallic and laminated composite plates. Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia (1994)

  24. Sathyamoorthy, M.: Nonlinear Analysis of Structures. CRC Press, New York (1997)

    MATH  Google Scholar 

  25. Nayfeh, A.H.: Nonlinear Interactions. Wiley, New York (2000)

    MATH  Google Scholar 

  26. Amabili, M., Carra, S.: Experiments and simulations for large-amplitude vibrations of rectangular plates carrying concentrated masses. J. Sound Vib. 331(1), 155–166 (2012)

    Article  Google Scholar 

  27. Purohit, A., Darpe, A.K., Singh, S.P.: Experimental investigations on flow induced vibration of an externally excited flexible plate. J. Sound Vib. 371, 237–251 (2016)

    Article  Google Scholar 

  28. Navazi, H.M., Nokhbatolfoghahaei, A., Ghobad, Y., Haddadpour, H.: Experimental measurement of energy density in a vibrating plate and comparison with energy finite element analysis. J. Sound Vib. 375, 289–307 (2016)

    Article  Google Scholar 

  29. Lu, S.F., Zhang, W., Chen, L.H.: Nonlinear dynamics modeling of axially moving cantilever laminated composite plates. International Conference on Mechanic Automation, pp. 1427–1430 (2011)

  30. Carrera, E.: Layer-wise mixed models for accurate vibration analysis of multilayered plates. J. Appl. Mech. 65(4), 820–828 (1998)

    Article  Google Scholar 

  31. Hao, Y.X., Zhang, W., Yang, J.: Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method. Compos. Part B-Eng. 42, 402–413 (2011)

    Article  Google Scholar 

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 11472068) and the General Scientific Research Program of Education Department of Liaoning Province (L2015430).

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Authors and Affiliations

  1. School of Energy and Power Engineering, Shenyang University of Chemical Technology, 11th street, Shenyang Economic and Technological Development District, Shenyang, China

    Z. X. Yang & Z. H. Jin

  2. School of Mechanical Engineering, Dalian University of Technology, No.2, Linggong Road, Dalian, China

    Q. K. Han & Y. G. Chen

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  1. Z. X. Yang
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  2. Q. K. Han
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  3. Y. G. Chen
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  4. Z. H. Jin
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Correspondence to Z. X. Yang.

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Yang, Z.X., Han, Q.K., Chen, Y.G. et al. Nonlinear harmonic response characteristics and experimental investigation of cantilever hard-coating plate. Nonlinear Dyn 89, 27–38 (2017). https://doi.org/10.1007/s11071-017-3433-1

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