Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibrations of fluid conveying microbeams under non-ideal boundary conditions

  • Atci, Duygu (Department of Mechanical Engineering, Manisa Celal Bayar University) ;
  • Bagdatli, Suleyman Murat (Department of Mechanical Engineering, Manisa Celal Bayar University)
  • Received : 2016.12.02
  • Accepted : 2017.03.17
  • Published : 2017.06.10
⟨ Previous Next ⟩

Abstract

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

Keywords

Acknowledgement

Supported by : Scientific and Technological Research Council of Turkey (TUBITAK)

References

  1. Akgoz, B. and Civalek, O. (2013a), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., Int. J., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
  2. Akgoz, B. and Civalek, O. (2013b), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020
  3. Akgoz, B. and Civalek, O. (2015a), "A novel microstructuredependent shear deformable pipes conveying fluid", Int. J. Mech. Sci., 99, 10-20. https://doi.org/10.1016/j.ijmecsci.2015.05.003
  4. Akgoz, B. and Civalek, O. (2015b), "Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity", Comp. Struct., 134, 294-301. https://doi.org/10.1016/j.compstruct.2015.08.095
  5. Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronautica, 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021
  6. Ansari, R., Gholami, R., Norouzzadeh, A. and Sahmani, S. (2015), "Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory", Microfluid. Nanofluid., 19(3), 509-522. https://doi.org/10.1007/s10404-015-1577-1
  7. Atci, D. and Bagdatli, S.M. (2017), "Vibrations of fluid conveying microbeams under non-ideal boundary conditions", Microsyst. Technol., 1-12. DOI: 10.1007/s00542-016-3255-y
  8. Bagdatli, S.M. and Uslu, B. (2015), "Free vibration analysis of axially moving beam under non-ideal conditions", Struct. Eng. Mech., Int. J., 54(3), 597-605. https://doi.org/10.12989/sem.2015.54.3.597
  9. Bagdatli, S.M., Ozkaya, E. and Oz, H.R. (2013), "Dynamics of axially accelerating beams with multiple supports", Nonlin. Dyn., 74(1-2), 237-255. https://doi.org/10.1007/s11071-013-0961-1
  10. Baohui, L., Hangshan, G., Yongshou, L. and Zhufeng, Y. (2012), "Free vibration analysis of micro pipe conveying fluid by wave method", Results Physics, 2, 104-109. https://doi.org/10.1016/j.rinp.2012.08.002
  11. Chakraborty, G., Mallik, A.K. and Hatwal, H. (1998), "Non-linear vibration of a travelling beam", Int. J. Nonlin. Mech., 34(4), 655-670.
  12. Chong, A.C.M. and Lam, D.C.C. (1999), "Strain gradient plasticity effect in indentation hardness of polymers", J. Materials Res., 14(10), 4103-4110. https://doi.org/10.1557/JMR.1999.0554
  13. Ding, H. and Chen, L. (2011), "Natural frequencies of nonlinear vibration of axially moving beams", Nonlin. Dyn., 63(1), 125-134. https://doi.org/10.1007/s11071-010-9790-7
  14. Ekici, H.O. and Boyaci, H. (2007), "Effects of non-ideal boundary conditions on vibrations of micro beams", J. Vib. Control, 13(9-10), 1369-1378. https://doi.org/10.1177/1077546307077453
  15. Ellis, S.R.W. and Smith, C.W. (1968), "A thin plate analysis and experimental evaluation of couple stress effects", Exper. Mech., 7(9), 372-380. https://doi.org/10.1007/BF02326308
  16. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994), "Strain gradient plasticity: theory and experiment", Acta Metall. Mater., 42(2), 475-487. https://doi.org/10.1016/0956-7151(94)90502-9
  17. Hosseini, M. and Bahaadini, R. (2016), "Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory", Int. J. Eng. Sci., 101, 1-13. https://doi.org/10.1016/j.ijengsci.2015.12.012
  18. Ibrahim, R.A. (2010), "Overview of mechanics of pipes conveying fluids-Part I: Fundamental studies", J. Press. Vessel Tech., 132(3), 034001. https://doi.org/10.1115/1.4001271
  19. Ibrahim, R.A. (2011), "Mechanics of pipes conveying fluids-Part II: Applications and fluid elastic problems", J. Pressure Vessel Tech., 133(2), 024001. https://doi.org/10.1115/1.4001270
  20. Kesimli, A., Ozkaya, E. and Bagdatli, S.M. (2015), "Nonlinear vibrations of spring-supported axially moving string", Nonlin. Dyn., 81(3), 1523-1534. https://doi.org/10.1007/s11071-015-2086-1
  21. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2008), "The sizedependent natural frequency of Bernoulli-Euler micro-beams", Int. J. Eng. Sci., 46(5), 427-437. https://doi.org/10.1016/j.ijengsci.2007.10.002
  22. Kural, S. and Ozkaya, E. (2012), "Vibrations of an axially accelerating, multiple supported flexible beam", Struct. Eng. Mech., Int. J., 44(4), 521-538. https://doi.org/10.12989/sem.2012.44.4.521
  23. Kural, S. and Ozkaya, E. (2015), "Size-dependent vibrations of a micro-beam conveying fluid and resting on an elastic foundation", J. of Vib. Cont., 23(7), 1106-1114. DOI: 10.1177/1077546315589666.
  24. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  25. Lee, J. (2013), "Free vibration analysis of beams with non-ideal clamped boundary conditions", J. Mech. Sci. Tech., 27(2), 297-303. https://doi.org/10.1007/s12206-012-1245-2
  26. Li, L., Hu, Y., Li, X. and Ling, L. (2016), "Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory", Microfluidics and Nanofluidics, 20(5), 76. https://doi.org/10.1007/s10404-016-1739-9
  27. Ma, Q. and Clarke, D.R. (1995), "Size dependent hardness of silver single crystals", J. Materials Res., 10(04), 853-863. https://doi.org/10.1557/JMR.1995.0853
  28. Ma, H.M., Gao, X-L. and Reddy, J.N. (2008), "A microstructuredependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  29. McFarland, A.W. and Colton, J.S. (2005), "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng., 15(5), 1060-1067. https://doi.org/10.1088/0960-1317/15/5/024
  30. Mindlin, R.D. (1964), "Micro-structure in linear elasticity", Archive Rational Mech. Analy., 16(1), 51-78. https://doi.org/10.1007/BF00248490
  31. Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of couple stresses in linear elasticity", Arch. Ration. Mech. Anal., 11(1), 415-448. https://doi.org/10.1007/BF00253946
  32. Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, John Wiley & Sons, USA.
  33. Ni, Q., Zhang, Z.L. and Wang, L. (2011), "Application of the differential transformation method to vibration analysis of pipes conveying fluid", Appl. Math. Comp., 217(16), 7028-7038. https://doi.org/10.1016/j.amc.2011.01.116
  34. Paidoussis, M.P. and Li, G.X. (1993), "Pipes conveying fluid: A model dynamical problem", J. Fluids Struct., 7(2), 137-204. https://doi.org/10.1006/jfls.1993.1011
  35. Paidoussis, M.P., Semler, C., Wadham-Gagnon, M. and Saaid, S. (2007), "Dynamics of cantilevered pipes conveying fluid. Part 2: Dynamics of system with intermediate spring support", J. Fluids Struct., 23(4), 569-587. https://doi.org/10.1016/j.jfluidstructs.2006.10.009
  36. Pakdemirli, M. and Boyaci, H. (2001), "Vibrations of a stretched beam with non-ideal boundary conditions", Math. Comp. Appl., 6(3), 217-220.
  37. Pakdemirli, M. and Boyaci, H. (2002), "Effect of non-ideal boundary conditions on the vibrations of continuous systems", J. Sound Vib., 249(4), 815-823. https://doi.org/10.1006/jsvi.2001.3760
  38. Pakdemirli, M. and Boyaci, H. (2003), "Non-linear vibrations of a simple-simple beam with a non-ideal support in between", J. Sound Vib., 268, 331-341. https://doi.org/10.1016/S0022-460X(03)00363-8
  39. Park, S.K. and Gao, X-L. (2006), "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng., 16(11), 2355-2359. https://doi.org/10.1088/0960-1317/16/11/015
  40. Stolken, J.S. and Evans, A.G. (1998), "Microbend test method for measuring the plasticity length scale", Acta Materialia, 46(14), 5109-5115. https://doi.org/10.1016/S1359-6454(98)00153-0
  41. Thurman, A.L. and Mote, C.D. (1969), "Free, periodic, nonlinear oscillations of an axially moving strip", J. Appl. Mech., 36, 3.
  42. Toupin, R.A. (1962), "Elastic materials with couple-stresses", Arch. Ratio. Mech. Anal., 11(1), 385-414. https://doi.org/10.1007/BF00253945
  43. Wang, L. (2010), "Size-dependent vibration characteristics of fluid-conveying micro tubes", J. Fluids Struct., 26(4), 675-684. https://doi.org/10.1016/j.jfluidstructs.2010.02.005
  44. Wang, L. (2012), "Vibration analysis of nanotubes conveying fluid based on gradient elasticity theory", J. Vib. Control, 18(2), 313-320. https://doi.org/10.1177/1077546311403957
  45. Wang, L., Gan, J. and Ni, Q. (2013a), "Natural frequency analysis of fluid-conveying pipes in the ADINA system", J. Phys.: Conference Series, 448(1), 012014.
  46. Wang, L., Liu, H.T., Ni, Q. and Wu, Y. (2013b), "Flexural vibrations of micro scale pipes conveying fluid by considering the size effects of micro-flow and micro-structure", Int. J. Eng. Sci., 71, 92-101. https://doi.org/10.1016/j.ijengsci.2013.06.006
  47. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  48. Yin, L., Qian, Q. and Wang, L. (2011), "Strain gradient beam model for dynamics of microscale pipes conveying fluid", Appl. Math. Model., 35(6), 2864-2873. https://doi.org/10.1016/j.apm.2010.11.069
  49. Yurddas, A., Ozkaya, E. and Boyaci, H. (2012), "Nonlinear vibrations and stability analysis of axially moving strings having non-ideal mid-support conditions", J. Vib. Control, 20(4), 518-534. https://doi.org/10.1177/1077546312463760
  50. Yurddas, A., Ozkaya, E. and Boyaci, H. (2013), "Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions", Nonlin. Dyn., 73(3), 1223-1244. https://doi.org/10.1007/s11071-012-0650-5
  51. Zeighampour, H. and Tadi Beni, Y. (2014), "Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory", Physica E, 61, 28-39. https://doi.org/10.1016/j.physe.2014.03.011

Cited by

  1. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2017, https://doi.org/10.12989/sem.2021.77.2.217