Smart Structures and Systems

  • 제19권3호
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  • Pages.309-322
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  • 2017
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  • 1738-1584(pISSN)
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  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM

  • Mohammadimehr, M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Alimirzaei, S. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2016.05.10
  • 심사 : 2016.12.15
  • 발행 : 2017.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Ansari, R., Faghih Shojaei, M., Gholami, Mohammadi, R., Mohammadi, V. and Darabi, M.A. (2013), "Thermal postbuckling behavior of size-dependent functionally graded Timoshenko micro-beams", Int. J. Non-Linear Mech., 50, 127-135. https://doi.org/10.1016/j.ijnonlinmec.2012.10.010
  2. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  3. Chakraborty, A., Mahaptra, D.R. and Gopalakrishnan, S. (2002), "Investigated finite element analysis of free vibration and wave propagation in asymmetric composite beam with structural discontinuities", Compos. Struct., 55(1), 23-36. https://doi.org/10.1016/S0263-8223(01)00130-1
  4. Ghiasian, S.E., Kiani, Y. and Eslami, M.R. (2014), "Non-linear rapid heating of FGM beams", Int. J. Non-Linear Mech., 67, 74-84. https://doi.org/10.1016/j.ijnonlinmec.2014.08.006
  5. Ghorbanpour Arani, 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
  6. Ghorbanpour Arani, A., Haghparast, E. and Zarei, H.B.A. (2016), "Vibration of axially moving 3-phase CNTFPC plate resting on orthotropic foundation", Struct. Eng. Mech., 57(1), 105-126. https://doi.org/10.12989/sem.2016.57.1.105
  7. Ghorbanpour Arani, A., Amir, S., Shajari, A.R., Khoddami Maraghi, Z. and Mohammadimehr, M. (2012), "Electro-thermal non-local vibration analysis of embedded DWBNNTs", Proc. Ins. Mech. Eng., Part C: J. Mech. Eng. Sci., 226(5), 1410-1422. https://doi.org/10.1177/0954406211422619
  8. Ghorbanpour Arani, A., Mobarakeh, M.R., Shams, S., Mohammadimehr, M. (2012), "The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5
  9. Giannopoulos, I.G. and Kallivokas, G. (2014), "Mechanical properties of graphene based nanocomposites incorporating a hybrid interphase", Finite Element. Anal. Des., 90, 31-40. https://doi.org/10.1016/j.finel.2014.06.008
  10. Hemmatnezhad, M., Ansari, R. and Rahimi, G.H. (2013), "Largeamplitude free vibrations of functionally graded beams by means of a finite element formulation", Appl. Math. Model., 37(18), 8495-8504. https://doi.org/10.1016/j.apm.2013.03.055
  11. Heshmati, M. and Yas, M.H. (2013), "Vibrations of non-uniform functionally graded MWCNTs- polystyrene nano-composite beams under action of moving load", Mater. Des., 46, 206-218. https://doi.org/10.1016/j.matdes.2012.10.002
  12. Heshmati, M. and Yas, M.H. (2013), "Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nano-composite beams subjected to multi-moving loads", Mater. Des., 49, 894-904. https://doi.org/10.1016/j.matdes.2013.01.073
  13. Ishaquddin, M.D., Raveendranath, P. and Reddy, J.N. (2016), "Efficient coupled polynomial interpolation scheme for out-ofplane free vibration analysis of curved beams", Finite Element. Anal. Des., 110, 58-66. https://doi.org/10.1016/j.finel.2015.10.007
  14. Kahrobaiyan, M.H., Asghari, M. and Ahmadian, M.T. (2014), "Strain gradient beam element", Adv. Compos. Mater., 68, 63-75.
  15. Karimov, K.S., Abid, М., Saleem, M., Akhmedov, M., Bashir, M., Shafique, U. and Ali, M. (2014), "Temperature gradient sensor based on CNT composite", Physica B, 446, 39-42. https://doi.org/10.1016/j.physb.2014.04.018
  16. 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. Solid., 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  17. Lau, K.T., Gu, C., Gao, G.H., Ling, H.Y. and Reid, S. (2004), "Stretching process of single and multiwalled carbon nanotubes for nanocomposite", Appl. Carbon., 42(2), 426-428. https://doi.org/10.1016/j.carbon.2003.10.040
  18. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turk J. Eng. Environ. Sci., 37(1), 1-15.
  19. Mohammadimehr, M., Mohandes, M. and Moradi, M. (2016), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J.Vib. Control, 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513
  20. 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 modified strain gradient theory (MSGT), sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077
  21. 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
  22. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 36(9), 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  23. 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
  24. Reddy, J.N. (2004), An Introduction to nonlinear finite element analysis, Oxford University Press, Oxford, New York, USA.
  25. Reddy, J.N. (1987), "Mixed finite element models for laminated composite plate", J. Eng. Indus., 109, 39-45. https://doi.org/10.1115/1.3187092
  26. Sahmani, S. and Ansari, R. (2013), "Size-dependent buckling analysis of functionally graded third-order shears deformable micro-beams including thermal environment effect", Appl. Math. Model., 37(23), 9499-9515. https://doi.org/10.1016/j.apm.2013.04.051
  27. Sahmani, S., Aghdam, M.M. and Bahrami, M. (2015), "On the free vibration characteristics of postbuckled third-order shear deformable FGM nano-beams including surface effects", Compos. Struct., 121, 377-385. https://doi.org/10.1016/j.compstruct.2014.11.033
  28. Shen, H. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  29. 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
  30. Taati, E., Molaei Najafabadi, M. and Reddy, J.N. (2014), "Sizedependent generalized thermo elasticity model for Timoshenko micro-beams based on strain gradient and non-Fourier heat conduction theories", Compos. Struct., 116, 595-611. https://doi.org/10.1016/j.compstruct.2014.05.040
  31. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Vessel. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012
  32. Yas, M.H. and Heshmati, M. (2012), "Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load", Appl. Math. Model., 36(4), 1371-1394. https://doi.org/10.1016/j.apm.2011.08.037
  33. Zhang, B., He, Y., Liu, D., Gan, Z. and Shen, L. (2014), "Nonclassical Timoshenko beam element based on the strain gradient elasticity theory", Finite Element. Anal. Des., 79, 22-39. https://doi.org/10.1016/j.finel.2013.10.004
  34. Zhang, S., Yin, J., Zhang, H.W. and Chen, B.S. (2016), "A twolevel method for static and dynamic analysis of multi-layered composite beam and plate", Finite Element. Anal. Des., 11, 1-18.

피인용 문헌

  1. Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory 2018, https://doi.org/10.1016/j.ast.2018.01.010
  2. Dynamic stability analysis of microcomposite annular sandwich plate with carbon nanotube reinforced composite facesheets based on modified strain gradient theory pp.1530-7972, 2018, https://doi.org/10.1177/1099636218782770
  3. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2017, https://doi.org/10.12989/anr.2019.7.2.109
  4. Hydro-thermo-mechanical biaxial buckling analysis of sandwich micro-plate with isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets based on FSDT on elastic foundations vol.33, pp.4, 2017, https://doi.org/10.12989/scs.2019.33.4.509
  5. Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam vol.78, pp.2, 2021, https://doi.org/10.12989/sem.2021.78.2.117
  6. Free vibration analysis of carbon nanotube RC nanobeams with variational approaches vol.11, pp.2, 2021, https://doi.org/10.12989/anr.2021.11.2.157