Smart Structures and Systems

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Mechanical parameters detection in stepped shafts using the FEM based IET

  • Song, Wenlei (College of Mechanical & Electrical Engineering, Wenzhou University) ;
  • Xiang, Jiawei (College of Mechanical & Electrical Engineering, Wenzhou University) ;
  • Zhong, Yongteng (College of Mechanical & Electrical Engineering, Wenzhou University)
  • Received : 2017.02.13
  • Accepted : 2017.07.19
  • Published : 2017.10.25
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Abstract

This study suggests a simple, convenient and non-destructive method for investigation of the Young's modulus detection in stepped shafts which only utilizes the first-order resonant frequency in flexural mode and dimensions of structures. The method is based on the impulse excitation technique (IET) to pick up the fundamental resonant frequencies. The standard Young's modulus detection formulas for rectangular and circular cross-sections are well investigated in literatures. However, the Young's modulus of stepped shafts can not be directly detected using the formula for a beam with rectangular or circular cross-section. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formula to detect Young's modulus of stepped shafts. The numerical simulation performed by finite element method (FEM) to obtain enough simulation data for RSM analysis. After analysis and calculation, the relationship of flexural resonant frequencies, dimensions of stepped shafts and Young's modulus is obtained. Numerical simulations and experimental investigations show that the IET method can be used to investigate Young's modulus in stepped shafts, and the FEM simulation and RSM based IET formula proposed in this paper is applicable to calculate the Young's modulus in stepped shaft. The method can be further developed to detect mechanical parameters of more complicated structures using the combination of FEM simulation and RSM.

Keywords

Acknowledgement

Supported by : National Science Foundation of China, Zhejiang Provincial Natural Science Foundation of China

References

  1. Alfano, M. and Pagnotta, L. (2007), "A non-destructive technique for the elastic characterization of thin isotropic plates", Ndt. & E. Int., 40(2), 112-120. https://doi.org/10.1016/j.ndteint.2006.10.002
  2. ASTM, E. (2001), "Standard test method for dynamic Young's modulus, shear modulus, and Poisson's ratio by sonic resonance", Annual Book of ASTM Standards 2001.
  3. Bahr, O., Schaumann, P., Bollen, B. and Bracke, J. (2013), "Young's modulus and Poisson's ratio of concrete at high temperatures: Experimental investigations", Mater. Design, 45, 421-429. https://doi.org/10.1016/j.matdes.2012.07.070
  4. Behmanesh, I. and Moaveni, B. (2016), "Accounting for environmental variability, modeling errors, and parameter estimation uncertainties in structural identification", J. Sound. Vib., 374, 92-110. https://doi.org/10.1016/j.jsv.2016.03.022
  5. Chiu, C.C. and Case, E.D. (1991), "Elastic modulus determination of coating layers as applied to layered ceramic composites", Mat. Sci. Eng. A - Struct., 132, 39-47. https://doi.org/10.1016/0921-5093(91)90359-U
  6. De Oliveira, A.P.N., Vilches, E.S., Soler, V.C. and Villegas, F.A.G. (2012), "Relationship between Young's modulus and temperature in porcelain tiles", J. Eur. Ceram. Soc., 32(11), 2853-2858. https://doi.org/10.1016/j.jeurceramsoc.2011.09.019
  7. Guillot, F.M. and Trivett, D.H. (2011), "Complete elastic characterization of viscoelastic materials by dynamic measurements of the complex bulk and Young's moduli as a function of temperature and hydrostatic pressure", J. Sound. Vib., 330, 3334-3351. https://doi.org/10.1016/j.jsv.2011.02.003
  8. Hauert, A., Rossoll, A. and Mortensen, A. (2009), "Young's modulus of ceramic particle reinforced aluminium: Measurement by the Impulse Excitation Technique and confrontation with analytical models", Compos. Part. A-Appl. S., 40(4),524-529. https://doi.org/10.1016/j.compositesa.2009.02.001
  9. Jiang, B.Z, Xiang, J.W. and Wang, Y.X. (2016), "Rolling bearing fault diagnosis approach using probabilistic principal component analysis denoising and cyclic bispectrum", J. Vib. Control, 22(10), 2420-2433. https://doi.org/10.1177/1077546314547533
  10. Kubojima, Y., Kato, H., Tonosaki, M. and Sonoda, S. (2015), "Measuring young's modulus of a wooden bar using flexural vibration without measuring its weight", Bio Resources, 11(1), 800-810.
  11. Li, J., Hao, H., and Lo, J.V. (2015), "Structural damage identification with power spectral density transmissibility: numerical and experimental studies", Smart Struct. Syst., 15(1), 15-40. https://doi.org/10.12989/sss.2015.15.1.015
  12. Liu, J.X., Zhang, X.W. and Chen, X.F. (2016a), "Modeling and active vibration control of a coupling system of structure and actuators", J. Vib. Control, 22(2), 382-395. https://doi.org/10.1177/1077546314532860
  13. Lugovy, M., Slyunyayev, V., Orlovskaya, N., Mitrentsis, E., Aneziris, C.G., Graule, T. and Kuebler, J. (2016), "Temperature dependence of elastic properties of ZrB 2-SiC composites", Ceram. Int., 42(2),2439-2445. https://doi.org/10.1016/j.ceramint.2015.10.044
  14. Mei, C. and Sha, H. (2016), "Analytical and experimental study of vibrations in simple spatial structures", J. Vib. Control, 22(17), 3711-3735. https://doi.org/10.1177/1077546314565807
  15. Munoz-Abella, B., Rubio, L. and Rubio, P. (2012), "A nondestructive method for elliptical cracks identification in shafts based on wave propagation signals and genetic algorithms", Smart Struct. Syst., 10(1), 47-65. https://doi.org/10.12989/sss.2012.10.1.047
  16. Pabst, W., Gregorova, E., Klouzek, J., Klouzkova, A., Zemenova, P., Kohoutkova, M. and Vsiansky, D. (2016), "High-temperature Young's moduli and dilatation behavior of silica refractories", J. Eur. Ceram. Soc., 36(1), 209-220. https://doi.org/10.1016/j.jeurceramsoc.2015.09.020
  17. Popovics, J.S., Kolluru, S.V. and Shah, S.P. (2000), "Determining elastic properties of concrete using vibrational resonance frequencies of standard test cylinders", Cement, Concrete Aggr., 22(2), 81-89.
  18. Pradhan, R., Dhara, A.K., Panchadhyayee, P. and Syam, D. (2015), "Determination of Young's modulus by studying the flexural vibrations of a bar: experimental and theoretical approaches", Eur. J. Phys., 37(1), 015001. https://doi.org/10.1088/0143-0807/37/1/015001
  19. Roebben, G. and Omer, V.D.B. (2002), "Recent advances in the use of the impulse excitation technique for the characterisation of stiffness and damping of ceramics, ceramic coatings and ceramic laminates at elevated temperature", Key Eng. Mater., 206, 621-624.
  20. Roebben, G., Bollen, B., Brebels, A., Van Humbeeck, J. and Van der Biest, O. (1997), "Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature" Rev. Sci. Instrum., 68(12), 4511-4515. https://doi.org/10.1063/1.1148422
  21. Rupitsch, S.J., IIg, J., Sutor, A., Lerch, R. and Dollinger, M. (2011), "Simulation based estimation of dynamic mechanical properties for viscoelastic materials used for vocal fold models", J. Sound. Vib., 330(18), 4447-4459. https://doi.org/10.1016/j.jsv.2011.05.008
  22. Schmidt, R., Wicher, V. and Tilgner, R. (2005), "Young's modulus of moulding compounds measured with a resonance method", Polym. Test., 24(2), 197-203. https://doi.org/10.1016/j.polymertesting.2004.08.010
  23. Soltanimaleki, A., Foroutan, M. and Alihemmati, J., (2016), "Free vibration analysis of functionally graded fiber reinforced cylindrical panels by a three dimensional meshfree model", J. Vib. Control, 22(19), 4087-4098. https://doi.org/10.1177/1077546315570717
  24. Sousa, F.J., Dal Bo, M., Guglielmi, P.O., Janssen, R. and Hotza, D. (2014), "Characterization of Young's modulus and fracture toughness of albite glass by different techniques", Ceram. Int., 40(7), 10893-10899. https://doi.org/10.1016/j.ceramint.2014.03.085
  25. Spinner, S., Reichard, T.W. and Tefft, W.E., (1960), "A comparison of experimental and theoretical relations between young's modulus and the flexural and longitudinal resonance frequencies of uniform bars", J. Res. Natl. Bur. Stand. Phys. Chem., 64(2), 147-155.
  26. Swarnakar, A.K., Donzel, L., Vleugels, J. and Biest, O.V.D. (2009), "High temperature properties of ZnO ceramics studied by the impulse excitation technique", J. Eur. Ceram. Soc., 29(14), 2991-2998. https://doi.org/10.1016/j.jeurceramsoc.2009.04.039
  27. Tognana, S., Salgueiro, W., Somoza, A. and Marzocca, A. (2010), "Measurement of the Young's modulus in particulate epoxy composites using the impulse excitation technique", Mat. Sci. Eng. A-Struct., 527(18), 4619-4623. https://doi.org/10.1016/j.msea.2010.04.083
  28. Unal, O. (2016), "Optimization of shot peening parameters by response surface methodology", Surf. Coat. Tech., 305, 99-109. https://doi.org/10.1016/j.surfcoat.2016.08.004
  29. Wang, Y.M., Chen, X.F. and He, Z.J. (2011), "Daubechies wavelet finite element method and genetic algorithm for detection of pipe crack", Nondestruct. Test. Eva., 26(1), 87-99. https://doi.org/10.1080/10589759.2010.521826
  30. Xiang, J.W., Matsumoto, T. and Long, J.Q. (2013), "Identification of damage locations based on operating deflection shape", Nondestruct. Test. Eva., 28(2), 166-180 https://doi.org/10.1080/10589759.2012.716437
  31. Xiang, J.W., Matsumoto, T., Long, J.Q., Wang, Y.X. and Jiang, Z.S. (2012), "A simple method to detect cracks in beam-like structures", Smart Struct. Syst., 9(4), 335-353. https://doi.org/10.12989/sss.2012.9.4.335
  32. Xiang, J.W., Nackenhorst, U., Wang, Y.X., Jiang, Y.Y., Gao, H.F. and He, Y.M. (2014), "A new method to detect cracks in plate-like structures with though-thickness cracks", Smart Struct. Syst., 14(3), 397-418. https://doi.org/10.12989/sss.2014.14.3.397
  33. Yang, Z.B., Chen, X.F. and Jiang, Y.Y. (2014a), "Generalised local entropy analysis for crack detection in beam-like structures", Nondestruct. Test. Eva., 29(2), 133-153. https://doi.org/10.1080/10589759.2014.904312
  34. Yang, Z.B., Chen, X.F., Li, X., Jiang, Y.Y., Miao, H.H. and He, Z.J. (2014b), "Wave motion analysis in arch structures via wavelet finite element method", J. Sound. Vib., 333(2), 446-469. https://doi.org/10.1016/j.jsv.2013.09.011
  35. Yang, Z.B., Chen, X.F., Yu, J., Liu, R., Liu, Z.H. and He, Z.J. (2013), "A damage identification approach for plate structures based on frequency measurements", Nondestruct. Test. Eva., 28(4), 321-341. https://doi.org/10.1080/10589759.2013.801472
  36. Yang, Z.B., Radzienski, M., Kudela, P. and Ostachowicz, W. (2017a), "Fourier spectral-based modal curvature analysis and its application to damage detection in beams", Mech. Syst. Signal. Pr., 84, 763-781. https://doi.org/10.1016/j.ymssp.2016.07.005
  37. Yang, Z.B., Radzienski, M., Kudela, P., and Ostachowicz, W. (2017b). "Damage detection in beam-like composite structures via Chebyshev pseudo spectral modal curvature", Compos. Struct., 168, 1-12. https://doi.org/10.1016/j.compstruct.2017.01.087
  38. Zeng, X., Wen, S., Li, M. and Xie, G. (2014), "Estimating Young's modulus of materials by a new three-point bending method", Adv. Mater. Sci. Eng., 2014(1), 1-9.
  39. Zhang, E., Chazot, J.D., Antoni, J. and Hamdi, M. (2013), "Bayesian characterization of Young's modulus of viscoelastic materials in laminated structures", J. Sound. Vib., 332(16), 3654-3666. https://doi.org/10.1016/j.jsv.2013.02.032
  40. Zhang, X., Gao, D.Y., Liu, Y. and Du, X. (2015), "A multiresolution analysis based finite element model updating method for damage identification", Smart Struct. Syst., 16(1), 47-65. https://doi.org/10.12989/sss.2015.16.1.047
  41. Zhang, X.W., Chen, X.F., You, S.Q. and He, Z. (2015), "Active control of dynamic frequency responses for shell structures", J. Vib. Control, 21(14), 2813-2824. https://doi.org/10.1177/1077546313517588
  42. Zhang, X.W., Gao, R.X., Yan, R.Q., Chen, X.F., Sun, C. and Yang, Z.B. (2016b), "Multivariable wavelet finite elementbased vibration model for quantitative crack identification by using particle swarm optimization", J. Sound. Vib., 375, 200-216. https://doi.org/10.1016/j.jsv.2016.04.018

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