Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method
Source abstract
Abstract
This research deals with the dynamic instability analysis of double-walled carbon nanotubes (DWCNTs) conveying pulsating fluid under 2D magnetic fields based on the sinusoidal shear deformation beam theory (SSDBT). In order to present a realistic model, the material properties of DWCNTs are assumed viscoelastic using Kelvin–Voigt model. Considering the strain gradient theory for small scale effects, a new formulation of the SSDBT is developed through the Gurtin–Murdoch elasticity theory in which the effects of surface stress are incorporated. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The van der Waals interactions between the adjacent walls of the nanotubes are taken into account. The size dependent motion equations and corresponding boundary conditions are derived based on the Hamilton’s principle. The differential quadrature method in conjunction with Bolotin method is applied for obtaining the dynamic instability region. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of DWCNTs. The results depict that the surface stress effects on the dynamic instability of visco-DWCNTs are very significant. Numerical results of the present study are compared with available exact solutions in the literature. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems in advanced biomechanics applications with magnetic field as a parametric controller.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Composite Structure Analysis and Optimization · Mechanical and Optical Resonators
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (45)
Show source-provided references
1. Akgöz, B., Civalek, Ö.: A size-dependent shear deformation beam model based on the strain gradient elasticity theory. Int. J. Eng. Sci. 70, 1–14 (2013a). doi: 10.1016/j.ijengsci.2013.04.00410.1016/j.ijengsci.2013.04.004 ↗
2. Akgöz, B., Civalek, Ö.: Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory. Compos. Struct. 98, 314–322 (2013b). doi: 10.1016/j.compstruct.2012.11.02010.1016/j.compstruct.2012.11.020 ↗
3. Akgöz, B., Civalek, Ö.: Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory. Arch. Appl. Mech. 82(3), 423–443 (2012). doi: 10.1007/s00419-011-0565-510.1007/s00419-011-0565-5 ↗
4. Aydogdu, M.: A new shear deformation theory for laminated composite plates. Compos. Struct. 89(1), 94–101 (2009). doi: 10.1016/j.compstruct.2008.07.00810.1016/j.compstruct.2008.07.008 ↗
5. Bolotin, V.V.: The dynamic stability of elastic systems. In: The Dynamic Stability of Elastic Systems. Holden-Day, San Francisco (1964)
6. Civalek, Ö.: Harmonic differential quadrature-finite differences coupled approaches for geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation. J. Sound Vib. 294, 966–980 (2006). doi: 10.1016/j.jsv.2005.12.04110.1016/j.jsv.2005.12.041 ↗
7. Civalek, Ö.: Application ofdifferential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns. Eng. Struct. 26, 171–186 (2004). doi: 10.1016/j.engstruct.2003.09.00510.1016/j.engstruct.2003.09.005 ↗
8. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983). doi: 10.1063/1.33280310.1063/1.332803 ↗
9. Fu, Y., Bi, R., Zhang, P.: Nonlinear dynamic instability of double-walled carbon nanotubes under periodic excitation. Acta Mech. Solida Sin. 22(3), 206–212 (2009). doi: 10.1016/S0894-9166(09)60267-610.1016/S0894-9166(09)60267-6 ↗
10. Gheshlaghi, B., Hasheminejad, S.M.: Surface effects on nonlinear free vibration of nanobeams. Compos. B Eng. 42(4), 934–937 (2011). doi: 10.1016/j.compositesb.2010.12.02610.1016/j.compositesb.2010.12.026 ↗
11. Ghorbanpour Arani, A., Amir, S.: Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory. Phys. B 419, 1–6 (2013). doi: 10.1016/j.physb.2013.03.01010.1016/j.physb.2013.03.010 ↗
12. Ghorbanpour Arani, A., Kolahchi, R., Vossough, H.: Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory. Phys. B 407(21), 4281–4286 (2012). doi: 10.1016/j.physb.2012.07.01810.1016/j.physb.2012.07.018 ↗
13. Ghorbanpour Arani, A., Hashemian, M., Kolahchi, R.: Nonlocal Timoshenko beam model for dynamic stability of double-walled boron nitride nanotubes conveying nanoflow. Proc. Inst. Mech. Eng. (2013). doi: 10.1177/1740349913513449
14. Ghorbanpour Arani, A., Amir, S., Dashti, P., Yousefi, M.: Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect. Comput. Mater. Sci. 86, 144–154 (2014a). doi: 10.1016/j.commatsci.2014.01.04710.1016/j.commatsci.2014.01.047 ↗
15. Ghorbanpour Arani, A., Kolahchi, R., Hashemian, M.: Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories. Proc. Inst. Mech. Eng. 28(17), 3258–3280 (2014b). doi: 10.1177/095440621452727010.1177/0954406214527270 ↗
16. Gurtin, M., Ian Murdoch, A.: A continuum theory of elastic material surfaces. Arch. Rational. Mech. Anal. 57(4), 291–323 (1975). doi: 10.1007/BF0026137510.1007/BF00261375 ↗
17. Gurtin, M.E., Ian Murdoch, A.: Surface stress in solids. Int. J. Solids Struct. 14(6), 431–440 (1978). doi: 10.1016/0020-7683(78)90008-210.1016/0020-7683(78)90008-2 ↗
18. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354(6348), 56–58 (1991)10.1038/354056a0 ↗
19. Karama, M., Afaq, K.S., Mistou, S.: Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Int. J. Solids Struct. 40(6), 1525–1546 (2003). doi: 10.1016/S0020-7683(02)00647-910.1016/S0020-7683(02)00647-9 ↗
20. Kaviani, F., Mirdamadi, H.R.: Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertial gradient theory. Comput. Struct. 116, 75–87 (2013). doi: 10.1016/j.compstruc.2012.10.02510.1016/j.compstruc.2012.10.025 ↗
21. Khodami Maraghi, Z., Ghorbanpour Arani, A., Kolahchi, R., Amir, S., Bagheri, M.R.: Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid. Compos. B 45(1), 423–432 (2013). doi: 10.1016/j.compositesb.2012.04.06610.1016/j.compositesb.2012.04.066 ↗
22. Kiani, K.: Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model. Appl. Math. Model. 37(4), 1836–1850 (2013). doi: 10.1016/j.apm.2012.04.02710.1016/j.apm.2012.04.027 ↗
23. Kiani, K.: Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field. J. Phys. Chem. Solids 75(1), 15–22 (2014). doi: 10.1016/j.jpcs.2013.07.02210.1016/j.jpcs.2013.07.022 ↗
24. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003). doi: 10.1016/S0022-5096(03)00053-X10.1016/S0022-5096(03)00053-X ↗
25. Lanhe, W., Hongjun, W., Daobin, W.: Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method. Compos. Struct. 77(3), 383–394 (2007). doi: 10.1016/j.compstruct.2005.07.01110.1016/j.compstruct.2005.07.011 ↗
26. Lei, X.-W., Natsuki, T., Shi, J.-X., Ni, Q.-Q.: Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model. Compos. B 43(1), 64–69 (2012). doi: 10.1016/j.compositesb.2011.04.03210.1016/j.compositesb.2011.04.032 ↗
27. Lei, J., He, Y., Zhang, B., Gan, Z., Zeng, P.: Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory. Int. J. Eng. Sci. 72, 36–52 (2013a). doi: 10.1016/j.ijengsci.2013.06.01210.1016/j.ijengsci.2013.06.012 ↗
28. Lei, Y., Adhikari, S., Friswell, M.I.: Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams. Int. J. Eng. Sci. 66–67, 1–13 (2013b). doi: 10.1016/j.ijengsci.2013.02.00410.1016/j.ijengsci.2013.02.004 ↗
29. Lei, Y., Murmu, T., Adhikari, S., Friswell, M.I.: Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams. Eur. J. Mech. A 42, 125–136 (2013c). doi: 10.1016/j.euromechsol.2013.04.00610.1016/j.euromechsol.2013.04.006 ↗
30. Levinson, M.: A new rectangular beam theory. J. Sound Vib. 74(1), 81–87 (1981). doi: 10.1016/0022-460X(81)90493-410.1016/0022-460X(81)90493-4 ↗
31. Li, J., Wu, Z., Kong, X., Li, X., Wu, W.: Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups. Compos. Struct. 108, 767–778 (2014). doi: 10.1016/j.compstruct.2013.10.01110.1016/j.compstruct.2013.10.011 ↗
32. Liang, F., Su, Y.: Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect. Appl. Math. Model. 37(10–11), 6821–6828 (2013). doi: 10.1016/j.apm.2013.01.05310.1016/j.apm.2013.01.053 ↗
33. Lim, C., Li, C., Yu, J.-L.: Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach. Acta. Mech. Sin. 26(5), 755–765 (2010)10.1007/s10409-010-0374-z ↗
34. Malekzadeh, P., Shojaee, M.: Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams. Compos. B 52, 84–92 (2013). doi: 10.1016/j.compositesb.2013.03.04610.1016/j.compositesb.2013.03.046 ↗
35. Mindlin, R.D.: Second gradient of strain and surface-tension in linear elasticity. Int. J. Solids Struct. 1(4), 417–438 (1965). doi: 10.1016/0020-7683(65)90006-510.1016/0020-7683(65)90006-5 ↗
36. Mirramezani, M., Mirdamadi, H.R., Ghayour, M.: Innovative coupled fluid–structure interaction model for carbon nano-tubes conveying fluid by considering the size effects of nano-flow and nano-structure. Comput. Mater. Sci. 77, 161–171 (2013). doi: 10.1016/j.commatsci.2013.04.04710.1016/j.commatsci.2013.04.047 ↗
37. Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51(4), 745–752 (1984). doi: 10.1115/1.316771910.1115/1.3167719 ↗
38. Şimşek, M., Reddy, J.N.: Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. Int. J. Eng. Sci. 64, 37–53 (2013). doi: 10.1016/j.ijengsci.2012.12.00210.1016/j.ijengsci.2012.12.002 ↗
39. Soldatos, K.P.: A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech. 94(3–4), 195–220 (1992). doi: 10.1007/BF0117665010.1007/BF01176650 ↗
40. Terrones, M.: Science and technology of the twenty-first century: synthesis, properties, and applications of carbon nanotubes. Annu. Rev. Mater. Res. 33(1), 419–501 (2003). doi: 10.1146/annurev.matsci.33.012802.10025510.1146/annurev.matsci.33.012802.100255 ↗
41. Thai, H.-T., Vo, T.P.: A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams. Int. J. Eng. Sci. 54, 58–66 (2012). doi: 10.1016/j.ijengsci.2012.01.00910.1016/j.ijengsci.2012.01.009 ↗
42. Touratier, M.: An efficient standard plate theory. Int. J. Eng. Sci. 29(8), 901–916 (1991). doi: 10.1016/0020-7225(91)90165-Y10.1016/0020-7225(91)90165-Y ↗
43. Wang, L.: A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid. Phys. E 44(1), 25–28 (2011). doi: 10.1016/j.physe.2011.06.03110.1016/j.physe.2011.06.031 ↗
44. Wang, H., Dong, K., Men, F., Yan, Y.J., Wang, X.: Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix. Appl. Math. Model. 34(4), 878–889 (2010). doi: 10.1016/j.apm.2009.07.00510.1016/j.apm.2009.07.005 ↗
45. Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002). doi: 10.1016/S0020-7683(02)00152-X10.1016/S0020-7683(02)00152-X ↗