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Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers

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Abstract

A rotating cantilever sandwich-plate model with a pre-twisted and pre-set angle has been developed to investigate the vibrational behavior of an aero-engine turbine blade with thermal barrier coating (TBC) layers. The classic von Karman plate theory and the first-order shear deformation theory are applied to derive the energy equations of the rotating TBC blade, in which the geometric shapes, the work ambient temperature, and the TBC material properties are considered. The Chebyshev-Ritz method is used to obtain the nature frequency of the rotating TBC blade. For static frequency and modal analysis, the finite-element method (FEM) is also applied to compare and validate the results from the Chebyshev-Ritz method. A good agreement is found among these kinds of methods. For dynamic frequency, the results are analyzed in detail concerning the influence of system parameters such as the thickness of the TBC layer, the working temperature, and the pre-twisted and pre-set angle. Finally, the Campbell diagram is demonstrated to analyze the resonance property of the cantilever sandwich TBC blade model.

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References

  1. Leissa A, Jacob K I. Three-dimensional vibrations of twisted cantilevered parallelepipeds. J Appl Mech, 1986, 53: 614–618

    Article  Google Scholar 

  2. Rao J S, Gupta K. Free vibrations of rotating small aspect ratio pretwisted blades. Mech Mach Theory, 1987, 22: 159–167

    Article  Google Scholar 

  3. Yang S M, Tsao S M. Dynamics of a pre-twisted blade under nonconstant rotating speed. Comput Struct, 1997, 62: 47–66

    MATH  Google Scholar 

  4. Hu X X, Sakiyama T, Matsuda H, et al. Fundamental vibration of rotating cantilever blades with pre-twist. J Sound Vib, 2004, 271: 47–66

    Article  Google Scholar 

  5. Chandiramani N K, Shete C D, Librescu L I. Vibration of higherorder-shearable pretwisted rotating composite blades. Int J Mech Sci, 2003, 45: 2017–2041

    Article  MATH  Google Scholar 

  6. Oh S Y, Song O, Librescu L. Effects of pretwist and presetting on coupled bending vibrations of rotating thin-walled composite beams. Int J Solids Struct, 2003, 40: 1203–1224

    Article  MATH  Google Scholar 

  7. Swaminathan M, Rao J S. Vibrations of rotating, pretwisted and tapered blades. Mech Mach Theory, 1977, 12: 331–337

    Article  Google Scholar 

  8. Sinha S K, Turner K E. Natural frequencies of a pre-twisted blade in a centrifugal force field. J Sound Vib, 2011, 330: 2655–2681

    Article  Google Scholar 

  9. Yao M H, Chen Y P, Zhang W. Nonlinear vibrations of blade with varying rotating speed. Nonlinear Dynam, 2012, 68: 487–504

    Article  MathSciNet  MATH  Google Scholar 

  10. Yao M H, Zhang W, Chen Y P. Analysis on nonlinear oscillations and resonant responses of a compressor blade. Acta Mech, 2014, 225: 3483–3510

    Article  MathSciNet  MATH  Google Scholar 

  11. Sun J, Lopez Arteaga I, Kari L. General shell model for a rotating pretwisted blade. J Sound Vib, 2013, 332: 5804–5820

    Article  Google Scholar 

  12. Sun J, Lopez Arteaga I, Kari L. Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory. Compos Struct, 2013, 99: 276–287

    Article  Google Scholar 

  13. Sun J, Kari L, Lopez Arteaga I. A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton’s principle. J Sound Vib, 2013, 332: 1355–1371

    Article  Google Scholar 

  14. Ramesh M N V, Mohan Rao N. Free vibration analysis of pre-twisted rotating FGM beams. Int J Mech Mater Des, 2013, 9: 367–383

    Article  Google Scholar 

  15. Chen X, Hutchinson J W, Evans A G. Simulation of the high temperature impression of thermal barrier coatings with columnar microstructure. Acta Mater, 2004, 52: 565–571

    Article  Google Scholar 

  16. Torvik P J, Hansel J. Mechanical properties of a ceramic coating with VEM infiltration. J Eng Mater Technol, 2009, 131: 031003

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Casadei F, Bertoldi K, Clarke D R. Finite element study of multi-modal vibration damping for thermal barrier coating applications. Comp Mater Sci, 2013, 79: 908–917

    Article  Google Scholar 

  19. Ivancic F, Palazotto A. Experimental considerations for determining the damping coefficients of hard coatings. J Aerospace Eng, 2005, 18: 9–17

    Article  Google Scholar 

  20. Limarga A M, Duong T L, Gregori G, et al. High-temperature vibration damping of thermal barrier coating materials. Surf Coat Tech, 2007, 202: 693–697

    Article  Google Scholar 

  21. 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, 2004, 370: 412–416

    Article  Google Scholar 

  22. Abu Al-Rub R K, 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, 2010, 47: 2131–2142

    Article  MATH  Google Scholar 

  23. Dragomir-Stanciu D, Oprişan C, Ianuş G, et al. Study of the influence of ceramic thermal coating on the mechanical resistance of the blades of aircraft engines. Procedia Tech, 2014, 12: 329–333

    Article  Google Scholar 

  24. Evans A G, Hutchinson J W. The mechanics of coating delamination in thermal gradients. Surf Coat Tech, 2007, 201: 7905–7916

    Article  Google Scholar 

  25. Hutchinson J W, Evans A G. On the delamination of thermal barrier coatings in a thermal gradient. Surf Coat Tech, 2002, 149: 179–184

    Article  Google Scholar 

  26. Tawancy H M, Mohammad A I, Al-Hadhrami L M, et al. On the performance and failure mechanism of thermal barrier coating systems used in gas turbine blade applications: Influence of bond coat/superalloy combination. Eng Fail Anal, 2015, 57: 1–20

    Article  Google Scholar 

  27. Yang L, Liu Q X, Zhou Y C, et al. Finite element simulation on thermal fatigue of a turbine blade with thermal barrier coatings. J Mater Sci Tech, 2014, 30: 371–380

    Article  Google Scholar 

  28. Sze K Y, Chen S H, Huang J L. The incremental harmonic balance method for nonlinear vibration of axially moving beams. J Sound Vib, 2005, 281: 611–626

    Article  Google Scholar 

  29. Shen J H, Lin K C, Chen S H, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method. Nonlinear Dynam, 2008, 52: 403–414

    Article  MATH  Google Scholar 

  30. Xu Y, Li Y, Liu D. Response of fractional oscillators with viscoelastic term under random excitation. J Comput Nonlin Dynam, 2014, 9: 031015

    Article  Google Scholar 

  31. Xu Y, Li Y, Liu D. A method to stochastic dynamical systems with strong nonlinearity and fractional damping. Nonlinear Dynam, 2016, 83: 2311–2321

    Article  MathSciNet  MATH  Google Scholar 

  32. Zhou D, Cheung Y K, Au F T K, et al. Three-dimensional vibration analysis of thick rectangular plates using Chebyshev polynomial and Ritz method. Int J Solids Struct, 2002, 39: 6339–6353

    Article  MATH  Google Scholar 

  33. Li W L. Vibration analysis of rectangular plates with general elastic boundary supports. J Sound Vib, 2004, 273: 619–635

    Article  Google Scholar 

  34. Dozio L, Carrera E. Ritz analysis of vibrating rectangular and skew multilayered plates based on advanced variable-kinematic models. Compos Struct, 2012, 94: 2118–2128

    Article  Google Scholar 

  35. Alijani F, Amabili M. Nonlinear vibrations of laminated and sandwich rectangular plates with free edges. Part 1: Theory and numerical simulations. Compos Struct, 2013, 105: 422–436

    Article  Google Scholar 

  36. Ye T, Jin G, Su Z, et al. A unified Chebyshev-Ritz formulation for vibration analysis of composite laminated deep open shells with arbitrary boundary conditions. Arch Appl Mech, 2014, 84: 441–471

    Article  MATH  Google Scholar 

  37. Reddy J N, Chin C D. Thermomechanical analysis of functionally graded cylinders and plates. J Thermal Stresses, 1998, 21: 593–626

    Article  Google Scholar 

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Correspondence to DongXing Cao.

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Cao, D., Liu, B., Yao, M. et al. Free vibration analysis of a pre-twisted sandwich blade with thermal barrier coatings layers. Sci. China Technol. Sci. 60, 1747–1761 (2017). https://doi.org/10.1007/s11431-016-9011-5

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  • DOI: https://doi.org/10.1007/s11431-016-9011-5

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