Smart Structures and Systems

  • 제18권5호
  • /
  • Pages.1029-1062
  • /
  • 2016
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear vibration analysis of MSGT boron-nitride micro ribbon based mass sensor using DQEM

  • Mohammadimehr, M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Monajemi, Ahmad A. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2016.01.26
  • 심사 : 2016.05.17
  • 발행 : 2016.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Akgoz, B. and Civalek, O. (2011), "Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams", Int. J. Eng. Sci., 49(11), 1268-1280. https://doi.org/10.1016/j.ijengsci.2010.12.009
  2. Akgoz, B. and Civalek, O. (2013), "Free vibration analysis of axially functionally graded tapered Brnoulli? Euler micro beams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020
  3. Amiri Moghadam, A.A., Kouzani, A., Zamani, R., Magniez, K. and Kaynak, A. (2015), "Nonlinear large deformation dynamic analysis of electroactive polymer actuators", Smart Struct. Syst., 15(6), 1601-1623. https://doi.org/10.12989/sss.2015.15.6.1601
  4. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16.1.081
  5. Bellman, R., Kashef, B.G. and Casti, J. (1972), "Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations", J. Comput. Phys., 10(1), 40-52. https://doi.org/10.1016/0021-9991(72)90089-7
  6. Chen, C.N. (2001), "Vibration of non-uniform shear deformable axisymmetric orthotropic circular plates solved by DQEM", Compos. Struct., 53(3), 257-264. https://doi.org/10.1016/S0263-8223(01)00009-5
  7. Chen, C.N. (2002), "DQEM vibration analyses of non-prismatic shear deformable beams resting on elastic foundations", J. Sound Vib., 255(5), 989-999. https://doi.org/10.1006/jsvi.2001.4176
  8. Chen, C.N. (2005), "DQEM analysis of in-plane vibration of curved beam structures", Adv. Eng. Software., 36(6), 412-424. https://doi.org/10.1016/j.advengsoft.2004.12.006
  9. Chen, C.N. (2008), "DQEM analysis of out-of-plane vibration of nonprismatic curved beam structures considering the effect of shear deformation", Adv. Eng. Software, 39(6), 466-472. https://doi.org/10.1016/j.advengsoft.2007.05.010
  10. Chowdhury, R., Adhikari, S. and Mitchell, J. (2009), "Vibrating carbon nanotube based bio sensors", Physica E., 42(2), 104-109. https://doi.org/10.1016/j.physe.2009.09.007
  11. Ejike, U.B.C.O. (1969), "The plane circular crack problem in the linearized couple-stress theory", J .Eng. Sci., 7(9), 947-961. https://doi.org/10.1016/0020-7225(69)90086-X
  12. Eringen, A.C. and Edelen, D.B.G. (1972), "On nonlocal elasticity", J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  13. Fleck, N.A. and Hutchinson, J.W. (1997), "Strain gradient plasticity", Adv. Appl. Mech., 33, 296-358.
  14. Fleck, N.A. and Hutchinson, J.W. (2001), "A reformulation of strain gradient plasticity", J. Mech. Phys. Solid., 49(10), 2245 -2271. https://doi.org/10.1016/S0022-5096(01)00049-7
  15. Fleck, N.A. and Hutchinson, J.W, (1993), "Phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solid., 41(12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N
  16. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013), "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", Int. J. Eng. Sci., 63, 52-60. https://doi.org/10.1016/j.ijengsci.2012.12.001
  17. GhorbanpourArani, A., Atabakhshian, V., Loghman, A., Shajari, A.R. and Amir, S. (2012), "Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method", Physica B., 407(13), 2549-2555. https://doi.org/10.1016/j.physb.2012.03.065
  18. Kahrobaiyan, M.H., Asghari, M., Rahaeifard, M. and Ahmadian, M.T. (2011), "A nonlinear strain gradient beam formulation", Int. J. Eng. Sci., 49(11), 1256-1267. https://doi.org/10.1016/j.ijengsci.2011.01.006
  19. Kahrobaiyan, M.H., Asghari, M. and Ahmadian, M.T. (2013), "Longitudinal behavior of strain gradient bars", Int. J. Eng. Sci., 44, 66-67.
  20. Ke, L.L., Wang, Y.S. and Wang, Z.D. (2012), "Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory", Compos. Struct., 94(6), 2038-2047. https://doi.org/10.1016/j.compstruct.2012.01.023
  21. Khalili, S.M.R., Jafari, A.A. and Eftekhari, S.A. (2010), "A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads", Compos. Struct., 92(10), 2497-2511. https://doi.org/10.1016/j.compstruct.2010.02.012
  22. 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
  23. Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P. (2013a), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J. Eng. Sci., 72, 36-52. https://doi.org/10.1016/j.ijengsci.2013.06.012
  24. Lei, Y., Murmu, T., Adhikari, S. and Friswell, M.I. (2013b), "Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams", Euro. J. Mech. A/Solids., 42, 125-136. https://doi.org/10.1016/j.euromechsol.2013.04.006
  25. Li, Y.S., Feng, W.J. and Cai, Z.Y. (2014), "Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory", Compos. Struct., 115, 41-50. https://doi.org/10.1016/j.compstruct.2014.04.005
  26. Malekzadeh, P., Karami, G. and Farid, M. (2004), "A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported", Comput. Methods Appl. Mech. Engrg, 193, 4781-4796. https://doi.org/10.1016/j.cma.2004.05.005
  27. Marinakis, M., Marinakis, Y. and Stavroulakis, G.E. (2011), "Vibration control of beams with piezoelectric sensors and actuators using particle swarm optimization", Expert. Sys. Appl., 38(6), 6872-6883. https://doi.org/10.1016/j.eswa.2010.12.037
  28. Mohammadi, H. and Mahzoon, M. (2013), "Thermal effects on postbuckling of nonlinear microbeams based on the modified strain gradient theory", Compos. Struct., 106, 764-776. https://doi.org/10.1016/j.compstruct.2013.06.030
  29. Mohammadimehr, M., Monajemi, A.A. and Moradi, M. (2015), "Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM", J. Mech. Sci. Technol., 29(6), 2297- 2305. https://doi.org/10.1007/s12206-015-0522-2
  30. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "The free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077
  31. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2016a), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007
  32. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2011), "Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory", J. Mech. Eng. Sci., 225(1), 498-506. https://doi.org/10.1177/2041298310392861
  33. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016b), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055
  34. Murmu, T. and Adhikari, S. (2013), "Nonlocal mass nanosensors based on vibrating monolayer graphene sheets", Sens. Actuat. B., 188, 1319- 1327. https://doi.org/10.1016/j.snb.2013.07.051
  35. Murmu, T. and Pradhan, S.C. (2009), "Small-scale effect on the vibration of non-uniform nano cantilever based on nonlocal elasticity theory", Physica E., 41(8), 1451-1456. https://doi.org/10.1016/j.physe.2009.04.015
  36. Narendar, S., Ravinder, S. and Gopalakrishnan, S. (2012), "Strain gradient torsional vibration analysis of micro/nano rods", Int. J. Nano Dimens., 3(1), 1-17.
  37. Rahmati, A.H. and Mohammadimehr, M. (2014), "Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM", Physica B., 440, 88-98. https://doi.org/10.1016/j.physb.2014.01.036
  38. Reddy, J.N. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids., 59(11), 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008
  39. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2-8), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  40. Shi, J.X., Ni, Q.Q., Lei, X.W. and Natsuki, T. (2011), "Nonlocal elasticity theory for the buckling of double-layer grapheme nanoribbons based on a continuum model", Comput.Mater. Sci., 50(11), 3085-3090. https://doi.org/10.1016/j.commatsci.2011.05.031
  41. Simsek, M. (2014), "Nonlinear static and free vibration analysis of microbeams based on the nonlinear elastic foundation using modified couple stress theory and He's variational method", Compos. Struct., 112, 264-272. https://doi.org/10.1016/j.compstruct.2014.02.010
  42. Torabi, K., Afshari, H. and Heidari-Rarani, M. (2013), "Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM", Eng. Solid Mech., 1(1), 9-20.
  43. Torabi, K., Afshari, H. and Haji Aboutalebi, F. (2014a), "A DQEM for transverse vibration analysis of multiple cracked non-uniform Timoshenko beams with general boundary conditions", Comput. Math. Appl., 67(3), 527-541. https://doi.org/10.1016/j.camwa.2013.11.010
  44. Torabi, K., Afshari, H. and Heidari-Rarani, M. (2014b), "Free vibration analysis of a rotating non-uniform blade with multiple open cracks using DQEM", Universal J. Mech. Eng., 2(3), 101-111. https://doi.org/10.13189/ujme.2014.020304
  45. Tounsi, A., Al-Basyouni, K.S. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  46. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnol., 18(10), 9-18.
  47. Wang, Y.G., Gao, D. and Wang, X.Z. (2008), "On the nonlinear vibration of heated corrugated circular plates with shallow sinusoidal corrugations", Int. J. Mech. Sci., 50(6), 1089-2008.
  48. Wang, Y.G., Lin, W.H. and Liu, N. (2013), "Nonlinear free vibration of a microscale beam based on modified couple stress theory", Physica E., 47, 80-85. https://doi.org/10.1016/j.physe.2012.10.020
  49. Xia, W., Wang, L. and Yin, L. (2010), "Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration", Int. J. Eng. Sci., 48(12), 2044-2053. https://doi.org/10.1016/j.ijengsci.2010.04.010
  50. 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
  51. Ying, Z.G., Ni, Y.Q. and Duan, Y.F. (2015), "Stochastic micro-vibration response characteristics of a sandwich plate with MR visco-elastomer core and mass", Smart Struct. Syst., 16(1), 141-162. https://doi.org/10.12989/sss.2015.16.1.141

피인용 문헌

  1. Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation vol.231, pp.8, 2016, https://doi.org/10.1007/s00707-020-02697-5