Biomaterials and Biomechanics in Bioengineering

  • 제5권1호
  • /
  • Pages.1-10
  • /
  • 2020
  • /
  • 2465-9835(pISSN)
  • /
  • 2465-9959(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Modeling free vibration analysis of osteon as bone unite

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Zokaee, Farin (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2019.04.04
  • 심사 : 2019.10.05
  • 발행 : 2020.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper investigated vibrational behavior of the osteon as bone unit in the different situations. This study can lead to increase our knowledge of our body. In this paper free vibration of the osteon with considering it as composite material has been studied. The effect of numbers of lamellae and radius of those on natural frequency of osteon are subtle; while thickness of lamellae have decreasing trend on natural frequency of osteon. The presence of nerve and blood in haversian canal change trend of natural frequency, absolutely. Using the nonlocal strain gradient theory(NSGT) leads to effectiveness of scale parameter on equations of motion and the obtained results. The governing equations are derived by Hamilton's principles. A parametric study is presented to examine the effect of various parameters on vibrational behaviour of osteon. The results can also be regarded as a benchmark in vibration analysis behavior of osteon as bone unite.

키워드

참고문헌

  1. Bakhadda, B., Bachir Bouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311.
  2. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103.
  3. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061.
  4. Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1.
  5. Civalek, O. (2017), "Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method", Compos. B Eng., 111, 45-59. https://doi.org/10.1016/j.compositesb.2016.11.030.
  6. Civalek, O. and Acar, M. (2007), "Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations", Int. J. Press. Vessel Pip., 84(9), 527-535. https://doi.org/10.1016/j.compositesb.2016.11.030.
  7. Cowin, S. (2001), Bone Mechanic Handbook, Second Edition, CRC, Washengton DC, Newyork.
  8. Currey, D.J. (2011), "The structure and mechanics of bone", Mater. Sci., 47, 41-54. https://doi.org/10.1007/s10853-011-5914-9.
  9. Currey, J.D., Pitchford, J.W. and Baxterand, P.D. (2006), "Variability of the mechanical properties of bone, and its evolutionary consequences", R. Soc., 27, 127-135. https://doi.org/10.1098/rsif.2006.0166.
  10. Demir, C. and Civalek, O. (2017), "A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix", Compos. Struct., 168, 872-884. https://doi.org/10.1016/j.compstruct.2017.02.091.
  11. Dullemeijer, P. and Fruitema, F. (1981), "The relation between osteon orientation and shear modulus", Netherlands J. Zool., 32(3), 300-306. https://doi.org/10.1163/002829681X00338.
  12. Ebrahimi, F., Zokaee, F. and Mahesh, V. (2019), "Analysis of the size-dependent wave propagation of a single lamellae based on the nonlocal strain gradient theory", Biomater. Biomech. Bioeng., 1(4), 45-58. https://doi.org/10.12989/bme.2019.4.1.045.
  13. Faingold, A., Cohen, S.R., Reznikov, N. and Wagner, H.D. (2013), "Osteonal lamellae elementary units: Lamellar microstructure, curvature and mechanical properties", Acta Biomater., 9, 5956-5962. https://doi.org/10.1016/j.actbio.2012.11.032.
  14. Hamed, E., Jasiuk, I., Yoo, A., Lee, Y. and Liszka, T. (2012), "Multi-scale modelling of elastic moduli of trabecular bone", J. R. Soc., 9, 1654-1673. https://doi.org/10.1098/rsif.2011.0814.
  15. Hamed, E., Lee, Y. and Jasiuk, I. (2010), "Multiscale modeling of elastic properties of cortical bone", Acta Mechanica, 213, 131-154. https://doi.org/10.1007/s00707-010-0326-5.
  16. Hassenkam, T., Fantner, G.E., Cutroni, J.A., Weaver, J.C., Morse, D.E. and Hansma, P.K. (2004), "Highresolution AFM imaging of intact and fractured trabecular bone", Bone., 35, 4-10. https://doi.org/10.1016/j.bone.2004.02.024.
  17. Henderson, J.P., Plummer, A. and Johnston, N. (2018), "An electro-hydrostatic actuator for hybrid activepassive vibration isolation", Int. J. Hydromechatron., 1(1), 47-71. https://doi.org/10.1504/IJHM.2018.090305
  18. Hoffler, C.E., Moore, K.E., Kozloff, K., Zysset, P.K., Brown, M.B. and Goldstein, S.A. (2000), "Heterogeneity of bone lamellar-level elastic moduli", Bone., 26(6), 603-609. https://doi.org/10.1016/S8756-3282(00)00268-4.
  19. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  20. Korsa, R. and Tomas, M. (2012), "Numerical identification of orthotropic coefficients of the lamella of a bone's osteon", Bull. Appl. Mech., 8(31), 45-53.
  21. Korsa, R., Lukes, J., Sepitka, J. and Mares, T. (2014), "Elastic properties of human osteon and osteonal lamella computed by a bidirectional micromechanical model and validated by nanoindentation", J. Biomech. Eng.,137(8), 081002. https://doi.org/10.1115/1.4030407.
  22. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  23. Liu, D., Weiner, S. and Wagner, H.D. (1999), "Anisotropic mechanical properties of lamellar bone using miniature cantilever bending specimens", J. Biomech., 32, 647-654. https://doi.org/10.1016/S0021-9290(99)00051-2.
  24. Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocalelasticity using the method of HDQ", Compos. Part B., 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067.
  25. Mitchell, J. and van Heteren, A.H. (2016), "A literature review of the spatial organization of lamellar bone", Comptes Rendus Palevol, 15(1-2), 23-31. https://doi.org/10.1016/j.crpv.2015.04.007.
  26. Mohammadimehr, M. and Shahedi, S. (2017), "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B., 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040.
  27. Mokhtari, F. and Beni, Y.T. (2016), "Free vibration analysis of microtubules as orthotropic elastic shells using stress and strain gradient elasticity theory", J. Solid. Mech., 8(3), 511-529.
  28. Ranglin, S., Das, D., Mingo, A., Ukinamemen, O., Gailani, G., Cowin, S. and Cardoso, L. (2009), "Development of a mechanical system for osteon isolation", Proceedings of the ASEE Mid-Atlantic Conference, PA, October.
  29. Ren, L., Yang, P., Wang, Z., Zhang, J., Ding, C. and Shang, P. (2015), "Biomechanical and biophysical environment of bone from the macroscopic to the pericellular and molecular level", J. Mech. Behav. Biomed. Mater., 50, 104-122. https://doi.org/10.1016/j.jmbbm.2015.04.021.
  30. Rho, J.Y., Kuhn-Spearing, L. and Zioupos, P. (1998), "Mechanical properties and the hierarchical structure of bone", Med. Eng. Phys., 20, 92-102. https://doi.org/10.1016/S1350-4533(98)00007-1.
  31. Sun, X., Zhao, H., Yu, Y., Zhang, S., Ma, Z., Li, N., ... & Hou, P. (2016), "Variations of mechanical property of out circumferential lamellae in cortical bone along the radial by nanoindentation", AIP Adv., 6, 115116. https://doi.org/10.1063/1.4968179.
  32. Tanaka, Y. (2018), "Active vibration compensator on moving vessel by hydraulic parallel mechanism", Int. J. Hydromechatron., 1(3), 350-359. https://doi.org/10.1504/ijhm.2018.094887
  33. Unal, M., Cingoz, F., Bagcioglu, C., Sozer, Y. and Akkus, O. (2018), "Interrelationships between electrical, mechanical and hydration properties of cortical bone", J. Mech. Behav. Biomed. Mater., 77, 12-23. https://doi.org/10.1016/j.jmbbm.2017.08.033.
  34. Vercher, A., Giner, E., Arango, C., Tarancon, J.E. and Fuenmayor, F.J. (2013), "Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models", Biomech. Model. Mechanobiol., 13(2), 437-449. https://doi.org/10.1007/s10237-013-0507-y.
  35. Wang, Z., Xie, Z. and Huang, W. (2018), "A pin-moment model of flexoelectric actuators", Int. J. Hydromech., 1(1), 72-90. https://doi.org/10.1504/IJHM.2018.090306
  36. Weiner, S., Wolfie, T. and Wagner, H.D. (1999), "Lamellar bone: Structure-function relations", J. Struct. Biol., 126, 241-255. https://doi.org/10.1006/jsbi.1999.4107.
  37. Xie, S., Manda, K., Wallace, R.J., Levrero-Florencio, F., Simpson, A.H.R. and Pankaj, P. (2017), "Time dependent behaviour of trabecular bone at multiple load levels", Ann. Biomed. Eng., 45(5), 1219-1226. https://doi.org/10.1007/s10439-017-1800-1.
  38. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  39. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.1016/j.compositesb.2018.09.051.