DOI QR코드

DOI QR Code

Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection 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 : 2015.05.21
  • 심사 : 2016.04.11
  • 발행 : 2016.08.10

초록

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Akbas, S.D. (2015), "Large deflection analysis of edge cracked simple supported beams", Struct. Eng. Mech., 54(3), 433-451 https://doi.org/10.12989/sem.2015.54.3.433
  2. Ansari, R. and Ramezannezhad, S. (2011), "Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects", Physica. E., 43, 1171-1178. https://doi.org/10.1016/j.physe.2011.01.024
  3. Bouiadjra, B.B., Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  4. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028
  5. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37, 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  6. Farshidianfar, A. and Soltani, P. (2012), "Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection", Comput. Mater. Sci., 53, 105-116. https://doi.org/10.1016/j.commatsci.2011.08.014
  7. 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, 2549-2555. https://doi.org/10.1016/j.physb.2012.03.065
  8. 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
  9. 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, 8-426.
  10. Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48(3), 415-434. https://doi.org/10.12989/sem.2013.48.3.415
  11. Li, Z.M. (2014), "Thermal post buckling behavior of 3D braided beams with initial geometric imperfection under different type temperature distributions", Compos. Struct., 108, 924-936. https://doi.org/10.1016/j.compstruct.2013.10.028
  12. Liew, K.M., Lei, Z.X. and Zhan, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites", A Review, Compos. Struct., 120,90-97. https://doi.org/10.1016/j.compstruct.2014.09.041
  13. Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B: Eng., 94(1), 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030
  14. 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, 1-15.
  15. Mohammadimehr, M., Mohandes, M. and Moradi, M. (2016a), "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
  16. Mohammadimehr, M., Monajemi, A.A. and Moradi, M. (2015a), "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
  17. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015b), "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
  18. 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
  19. 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, 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  20. Putcha, N.S. and Refined, A. (1986), "Mixed shear flexible finite element for the nonlinear analysis of laminated plates",Comput. Struct., 22, 529-538. https://doi.org/10.1016/0045-7949(86)90002-7
  21. 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
  22. Ranjan, R. (2011), "Nonlinear finite element analysis of bending of straight beams using hp-spectral approximations", J. Solid. Mech., 3, 96-113.
  23. 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
  24. Reddy, J.N. (2004), An Introduction to nonlinear finite element analysis, Oxford University Press, Oxford, New York, USA.
  25. 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., 12, 264-272.
  26. Wang, B., Deng, Z., Ouyang, H. and Zhou, J. (2015), "Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory", Physica. E., 66, 283-292. https://doi.org/10.1016/j.physe.2014.09.015
  27. Wang, B., Deng, Z.C. and Zhang, K. (2013), "Nonlinear vibration of embedded single walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory", Appl. Math. Mech., Engl. Ed. (English Edition), 34(3), 269-280. https://doi.org/10.1007/s10483-013-1669-8
  28. 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, 1371-1394. https://doi.org/10.1016/j.apm.2011.08.037
  29. 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. Ves. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012

피인용 문헌

  1. The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow vol.510, 2017, https://doi.org/10.1016/j.physb.2017.01.014
  2. Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings 2017, https://doi.org/10.1177/1077546317706887
  3. Post-buckling analysis of piezo-magnetic nanobeams with geometrical imperfection and different piezoelectric contents pp.1432-1858, 2018, https://doi.org/10.1007/s00542-018-4241-3
  4. Nonlinear free vibration of FG-CNT reinforced composite plates vol.64, pp.3, 2016, https://doi.org/10.12989/sem.2017.64.3.381
  5. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.109
  6. Postbuckling of Curved Carbon Nanotubes Using Energy Equivalent Model vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.136
  7. Free vibration of Cooper-Naghdi micro saturated porous sandwich cylindrical shells with reinforced CNT face sheets under magneto-hydro-thermo-mechanical loadings vol.70, pp.3, 2016, https://doi.org/10.12989/sem.2019.70.3.351
  8. Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.431
  9. Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution vol.24, pp.6, 2016, https://doi.org/10.12989/cac.2019.24.6.499
  10. Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM vol.8, pp.1, 2016, https://doi.org/10.12989/anr.2020.8.1.059
  11. Analysis of porous micro sandwich plate: Free and forced vibration under magneto-electro-elastic loadings vol.8, pp.1, 2016, https://doi.org/10.12989/anr.2020.8.1.069
  12. Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors vol.25, pp.3, 2016, https://doi.org/10.12989/cac.2020.25.3.215
  13. Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory vol.62, pp.None, 2020, https://doi.org/10.4028/www.scientific.net/jnanor.62.108
  14. Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.229
  15. Forced Axial Vibration of a Single-Walled Carbon Nanotube Embedded in Elastic Medium under Various Moving Forces vol.63, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.63.112
  16. Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation vol.25, pp.6, 2020, https://doi.org/10.12989/cac.2020.25.6.485
  17. Nonlinear stability of smart nonlocal magneto-electro-thermo-elastic beams with geometric imperfection and piezoelectric phase effects vol.25, pp.6, 2020, https://doi.org/10.12989/sss.2020.25.6.707
  18. Vibration behavior of a micro cylindrical sandwich panel reinforced by graphene platelet vol.26, pp.13, 2016, https://doi.org/10.1177/1077546319892730
  19. Analyzing exact nonlinear forced vibrations of two-phase magneto-electro-elastic nanobeams under an elliptic-type force vol.9, pp.1, 2016, https://doi.org/10.12989/anr.2020.9.1.047
  20. Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FG-SWCNTs based on a nonlocal strain gradient theory vol.26, pp.1, 2016, https://doi.org/10.12989/cac.2020.26.1.031
  21. Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation vol.26, pp.1, 2016, https://doi.org/10.12989/cac.2020.26.1.053
  22. Free vibration of sandwich micro-beam with porous foam core, GPL layers and piezo-magneto-electric facesheets via NSGT vol.26, pp.1, 2016, https://doi.org/10.12989/cac.2020.26.1.075
  23. 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
  24. Nano research for investigating the effect of SWCNTs dimensions on the properties of the simulated nanocomposites: a molecular dynamics simulation vol.9, pp.2, 2020, https://doi.org/10.12989/anr.2020.9.2.083
  25. Vibration control of sandwich plate-reinforced nanocomposite face sheet and porous core integrated with sensor and actuator layers using perturbation method vol.27, pp.15, 2021, https://doi.org/10.1177/1077546320948330
  26. Effects of the Molecular Weight of PCz on Selective Extraction of Large-Diameter Semiconducting Single-Walled Carbon Nanotubes vol.69, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.69.11
  27. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2016, https://doi.org/10.12989/amr.2021.10.3.169
  28. Perturbation Method for Thermal Post-Buckling Analysis of Shear Deformable FG-CNTRC Beams with Different Boundary Conditions vol.21, pp.13, 2021, https://doi.org/10.1142/s0219455421501753