Advances in nano research

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Analytical and mathematical simulation for nonlinear stability of scale-dependent magneto-electro-elastic system

  • Li, Bin (School of Mechanical Engineering, Wuhan Polytechnic University) ;
  • Xu, Xiaojia (School of Mechanical Engineering, Wuhan Polytechnic University) ;
  • Hu, Zhigang (School of Mechanical Engineering, Wuhan Polytechnic University) ;
  • Liu, Yuzuo (School of Mechanical Engineering, Wuhan Polytechnic University) ;
  • Qi, Menghui (Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology) ;
  • Zheng, Zengquan (Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology)
  • Received : 2021.03.20
  • Accepted : 2021.08.12
  • Published : 2021.10.25
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Abstract

By using differential quadrature method (DQM), a numerical investigation was provided for nonlinear stability behavior of magneto-electro-elastic (MEE) cylindrical shells at microscale. It is assumed that the cylindrical shell has been subjected to compressive loads leading to buckling phenomena in geometrically nonlinear regime. The non-uniformity of strain field has been inserted in the formulation for considering the microscale effects. The material properties of the shell are considered to be inhomogeneous with graded distribution. After solving the governing equations using DQM, it is realized that if the nanoscale shell is subjected to electrical and magnetic fields, the post-buckling path may be changed with the value of electrical voltage and magnetic potential. Also, strain gradient effects have remarkable influence on post-buckling curves and critical voltages.

Keywords

Acknowledgement

The work was supported by General scientific research projects of Wuhan Polytechnic University (2020Y11), This work was finished at Wuhan University of Technology (WUT) and Wuhan Polytechnic University, Wuhan.

References

  1. Ahmed, R.A., Al-Maliki, A.F. and Faleh, N.M. (2020a), "Dynamic characteristics of multi-phase crystalline porous shells with using strain gradient elasticity", Adv. Nano Res., 8(2), 157-167. https://doi.org/10.12989/anr.2020.8.2.157.
  2. Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020b), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. https://doi.org/10.12989/sem.2020.76.3.413.
  3. Ahmed, R.A., Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020c), "A review of effects of partial dynamic loading on dynamic response of nonlocal functionally graded material beams", Adv. Mater. Res., 9(1), 33-48. https://doi.org/10.12989/amr.2020.9.1.033.
  4. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057.
  5. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257-278. https://doi.org/10.12989/anr.2018.6.3.257.
  6. Barati, M.R. and Zenkour, A.M. (2018), "Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions", J. Vib. Control, 24(10), 1910-1926. https://doi.org/10.1177%2F1077546316672788. https://doi.org/10.1177%2F1077546316672788
  7. Barati, M.R. and Shahverdi, H. (2021), "Assessment of nonlinear vibrations of thin plates undergoing large deflection and moderate rotation using Jacobi elliptic functions", Mech. Based Des. Struct., 1-17. https://doi.org/10.1080/15397734.2021.1956329.
  8. Barretta, R., Feo, L., Luciano, R., de Sciarra, F.M. and Penna, R. (2016), "Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation", Compos. Part B Eng., 100, 208-219. https://doi.org/10.1016/j.compositesb.2016.05.052.
  9. Bich, D.H., Nguyen, N.X. and Van Tung, H. (2013), "Postbuckling of functionally graded cylindrical shells based on improved Donnell equations", Vietnam J. Mech., 35(1), 1-15. https://doi.org/10.15625/0866-7136/35/1/2894.
  10. Chen, C., Wang, X., Wang, Y., Yang, D., Yao, F., Zhang, W. and Hu, D. (2020), "Additive manufacturing of piezoelectric materials", Adv. Funct. Mater., 30(52), 2005141. https://doi.org/10.1002/adfm.202005141.
  11. Chikh, A., Bakora, A., Heireche, H., Houari, M.S.A., Tounsi, A. and Bedia, E.A. (2016), "Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory", Struct. Eng. Mech., 57(4), 617-639. https://doi.org/10.12989/sem.2016.57.4.617.
  12. Dai, Z., Xie, J., Fan, X., Ding, X., Liu, W., Zhou, S. and Ren, X. (2020), "Enhanced energy storage properties and stability of Sr (Sc0.5Nb0.5)O3 modified 0.65BaTiO3-0.35Bi0.5Na0.5TiO ceramics", Chem. Eng. J., 397, 125520. https://doi.org/10.1016/j.cej.2020.125520.
  13. Dai, Z., Guo, S., Gong, Y. and Wang, Z. (2021a), "Semiconductor flexoelectricity in graphite-doped SrTiO3 ceramics", Ceram. Int., 47(5), 6535-6539. https://doi.org/10.1016/j.ceramint.2020.10.239.
  14. Dai, Z., Xie, J., Chen, Z., Zhou, S., Liu, J., Liu, W. and Ren, X. (2021b), "Improved energy storage density and efficiency of (1-x)Ba0.85Ca0.15Zr0.1Ti0.9O3-xBiMg2/3NbO3 lead-free ceramics", Chem. Eng. J., 410, 128341. https://doi.org/10.1016/j.cej.2020.128341.
  15. Ebrahimi, F. and Barati, M.R. (2019a), "Hygrothermal effects on static stability of embedded single-layer graphene sheets based on nonlocal strain gradient elasticity theory", J. Therm. Stresses, 42(12), 1535-1550. https://doi.org/10.1080/01495739.2019.1662352.
  16. Ebrahimi, F. and Barati, M.R. (2019b), "On static stability of electro-magnetically affected smart magneto-electro-elastic nanoplates", Adv. Nano Res., 7(1), 63-75. http://doi.org/10.12989/anr.2019.7.1.063.
  17. Ebrahimi, F. and Barati, M.R. (2019c), "Dynamic modeling of embedded nanoplate systems incorporating flexoelectricity and surface effects", Microsyst. Technol., 25(1), 175-187. https://doi.org/10.1007/s00542-018-3946-7.
  18. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  19. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  20. Fang, J., Liu, C., Simos, T.E. and Famelis, I.T. (2020), "Neural network solution of single-delay differential equations", Mediterranean J. Math., 17(1), 1-15. https://doi.org/10.1007/s00009-019-1452-5.
  21. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039.
  22. Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2021), "Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading", Struct. Eng. Mech., 78(1), 15-22. https://doi.org/10.12989/sem.2021.78.1.015.
  23. Heydarpour, Y. and Malekzadeh, P. (2019), "Dynamic stability of cylindrical nanoshells under combined static and periodic axial loads", J. Brazil. Soc. Mech. Sci. Eng., 41(4), 184. https://doi.org/10.1007/s40430-019-1675-1.
  24. Ke, L.L. and Wang, Y. S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E, 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002.
  25. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart Mater. Struct., 23(12), 125036. https://doi.org/10.1088/0964-1726/23/12/125036.
  26. Kovalnogov, V.N., Simos, T.E., and Tsitouras, C. (2020), "Ninth-order, explicit, two-step methods for second-order inhomogeneous linear IVPs", Math. Method Appl. Sci., 43(7), 4918-4926. https://doi.org/10.1002/mma.6246.
  27. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013.
  28. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.
  29. Li, T., Dai, Z., Yu, M. and Zhang, W. (2021), "Numerical investigation on the aerodynamic resistances of double-unit trains with different gap lengths", Eng. Appl. Comput. Fluid Mech., 15(1), 549-560. https://doi.org/10.1080/19942060.2021.1895321.
  30. Lu, L., Guo, X. and Zhao, J. (2017), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006.
  31. Ma, L.H., Ke, L.L., Reddy, J.N., Yang, J., Kitipornchai, S. and Wang, Y.S. (2018), "Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory", Compos. Struct., 199, 10-23. https://doi.org/10.1016/j.compstruct.2018.05.061.
  32. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017a), "Calibration of nonlocal strain gradient shell model for buckling analysis of nanotubes using molecular dynamics simulations", Physica B, 521, 102-111. https://doi.org/10.1016/j.physb.2017.06.058.
  33. Mehralian, F., Beni, Y.T. and Zeverdejani, M.K. (2017b), "Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes", Physica B, 514, 61-69. https://doi.org/10.1016/j.physb.2017.03.030.
  34. Medvedev, M.A., Simos, T.E. and Tsitouras, C. (2020), "Explicit, Eighth-Order, Four-Step Methods for Solving y"= f(x,y)", Bull. Malaysian Math. Sci. Soc., 43(5), 3791-3807. https://doi.org/10.1007/s40840-019-00879-6.
  35. Medvedeva, M.A., Simos, T.E. and Tsitouras, C. (2021a), "Sixth-order, P-stable, Numerov-type methods for use at moderate accuracies", Math. Method. Appl. Sci., 44(8), 6923-6930. https://doi.org/10.1002/mma.7233.
  36. Medvedeva, M.A., Simos, T.E. and Tsitouras, C. (2021b), "Exponential integrators for linear inhomogeneous problems", Math. Method. Appl. Sci., 44(1), 937-944. https://doi.org/10.1002/mma.6802.
  37. Mirjavadi, S.S., Forsat, M., Badnava, S., Barati, M.R. and Hamouda, A.M.S. (2020a), "Nonlinear dynamic characteristics of nonlocal multi-phase magneto-electro-elastic nano-tubes with different piezoelectric constituents", Appl. Phys. A, 126(8), 1-16. https://doi.org/10.1007/s00339-020-03743-8.
  38. Mirjavadi, S.S., Yahya, Y.Z., Forsat, M., Khan, I., Hamouda, A.M. S. and Barati, M.R. (2020b), "Magneto-electric effects on nonlocal nonlinear dynamic characteristics of imperfect multiphase magneto-electro-elastic beams", J. Magnetism. Magnet. Mater., 503, 166649. https://doi.org/10.1016/j.jmmm.2020.166649.
  39. Mirjavadi, S.S., Bayani, H., Khoshtinat, N., Forsat, M., Barati, M. R. and Hamouda, A.M.S. (2020c), "On nonlinear vibration behavior of piezo-magnetic doubly-curved nanoshells", Smart Struct. Syst., 26(5), 631-640. https://doi.org/10.12989/sss.2020.26.5.631.
  40. Mirjavadi, S.S., Nikookar, M., Mollaee, S., Forsat, M., Barati, M. R. and Hamouda, A.M.S. (2020d), "Analyzing exact nonlinear forced vibrations of two-phase magneto-electro-elastic nanobeams under an elliptic-type force", Adv. Nano Res., 9(1), 47-58. https://doi.org/10.12989/anr.2020.9.1.047.
  41. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Hamouda, A.M.S. (2020e), "Porosity effects on post-buckling behavior of geometrically imperfect metal foam doubly-curved shells with stiffeners", Struct. Eng. Mech., 75(6), 701-711. https://doi.org/10.12989/sem.2020.75.6.701.
  42. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020g), "Assessment of transient vibrations of graphene oxide reinforced plates under pulse loads using finite strip method", Comput. Concrete, 25(6), 575-585. https://doi.org/10.12989/cac.2020.25.6.575.
  43. Mirjavadi, S.S., Forsat, M., Yahya, Y.Z., Barati, M.R., Jayasimha, A.N. and Khan, I. (2020h), "Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection", Adv. Concrete Constr., 9(4), 397-406. https://doi.org/10.12989/acc.2020.9.4.397.
  44. Muhammad, A.K., Hamad, L.B., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment", Adv. Mater. Res., 8(3), 237-257. https://doi.org/10.12989/amr.2019.8.3.237.
  45. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68(4), 608-618. https://doi.org/10.1115/1.1380385.
  46. Qiao, Y.X., Sheng, S.L., Zhang, L.M., Chen, J., Yang, L.L., Zhou, H.L. and Zheng, Z.B. (2021), "Friction and wear behaviors of a high nitrogen austenitic stainless steel Fe-19Cr-15Mn-0.66 N". J. Min. Metall, 57(2), 285-293. https://doi.org/10.2298/JMMB201026025Q.
  47. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Free vibration response of two-dimensional magneto-electro-elastic laminated plates", J. Sound Vib., 292(3-5), 626-644. https://doi.org/10.1016/j.jsv.2005.08.004.
  48. Sayyad, A.S. and Ghugal, Y.M. (2018), "An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation", Adv. Aircraft Spacecraft Sci., 5(6), 671-689. https://doi.org/10.12989/aas.2018.5.6.671.
  49. Shariati, A., Barati, M.R., Ebrahimi, F. and Toghroli, A. (2020a), "Investigation of microstructure and surface effects on vibrational characteristics of nanobeams based on nonlocal couple stress theory", Adv. Nano Res., 8(3), 191-202. https://doi.org/10.12989/anr.2020.8.3.191.
  50. Shariati, A., Barati, M.R., Ebrahimi, F., Singhal, A. and Toghroli, A. (2020b), "Investigating vibrational behavior of graphene sheets under linearly varying in-plane bending load based on the nonlocal strain gradient theory", Adv Nano Res., 8(4), 265-276. https://doi.org/10.12989/anr.2020.8.4.265.
  51. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.
  52. Simsek, M. (2019), "Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory", Compos. Struct., 224, 111041. https://doi.org/10.1016/j.compstruct.2019.111041.
  53. Simos, T.E. and Tsitouras, C. (2020), "Explicit, ninth order, two step methods for solving inhomogeneous linear problems x"(t) = Λx(t) + f(t)", Appl. Numer. Math., 153, 344-351. https://doi.org/10.1016/j.apnum.2020.03.003.
  54. Simos, T.E. and Tsitouras, C. (2021), "Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems", Numer. Algorithms, 87(2), 511-525. https://doi.org/10.1007/s11075-020-00976-9.
  55. Sun, J., Aslani, F., Wei, J. and Wang, X. (2021), "Electromagnetic absorption of copper fiber oriented composite using 3D printing", Constr. Build. Mater., 300, 124026. https://doi.org/10.1016/j.conbuildmat.2021.124026.
  56. Tan, L., Sun, Y., Wei, C., Tao, Y., Tian, Y., An, Y. and Feng, J. (2021), "Design of robust, lithiophilic, and flexible inorganic-polymer protective layer by separator engineering enables dendrite-free lithium metal batteries with LiNi0.8Mn0.1Co0.1O2 cathode", Small, 17(13), 2007717. https://doi.org/10.1002/smll.202007717.
  57. Uzun, B. and Civalek, O. (2019), "Free vibration analysis Silicon nanowires surrounded by elastic matrix by nonlocal finite element method", Adv. Nano Res., 7(2), 99-108. https://doi.org/10.12989/anr.2019.7.2.099.
  58. Waksmanski, N. and Pan, E. (2017), "An analytical three-dimensional solution for free vibration of a magneto-electro-elastic plate considering the nonlocal effect", J. Intell. Mater. Syst. Struct., 28(11), 1501-1513. https://doi.org/10.1177%2F1045389X16672734. https://doi.org/10.1177%2F1045389X16672734
  59. Xu, X. and Nieto-Vesperinas, M. (2019), "Azimuthal imaginary Poynting momentum density", Phys. Rev. Lett., 123(23), 233902. https://doi.org/10.1103/PhysRevLett.123.233902.
  60. Yan, D., Wang, W. and Chen, Q. (2020), "Fractional-order modeling and nonlinear dynamic analyses of the rotor-bearing-seal system", Chaos Soliton Fract., 133, 109640. https://doi.org/10.1016/j.chaos.2020.109640.
  61. Zeighampour, H., Beni, Y.T. and Dehkordi, M.B. (2018), "Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory", Thin Wall. Struct., 122, 378-386. https://doi.org/10.1016/j.tws.2017.10.037.
  62. Zhang, C. and Ou, J. (2015), "Modeling and dynamical performance of the electromagnetic mass driver system for structural vibration control", Eng. Struct., 82, 93-103. https://doi.org/10.1016/j.engstruct.2014.10.029.
  63. Zhang, X. and Zhang, Y. (2021a), "Experimental study on enhanced heat transfer and flow performance of magnetic nanofluids under alternating magnetic field. International journal of thermal sciences", 164, 106897. https://doi.org/10.1016/j.ijthermalsci.2021.106897.
  64. Zhang, X. and Zhang, Y. (2021b), "Heat transfer and flow characteristics of Fe3O4-water nanofluids under magnetic excitation", Int. J. Therm. Sci., 163, 106826. https://doi.org/10.1016/j.ijthermalsci.2020.106826.
  65. Zhao, X., Zhu, W.D. and Li, Y.H. (2020a), "Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions", J. Sound Vib., 481, 115407. https://doi.org/10.1016/j.jsv.2020.115407.
  66. Zhao, N., Deng, L., Luo, D. and Zhang, P. (2020b), "One-step fabrication of biomass-derived hierarchically porous carbon/MnO nanosheets composites for symmetric hybrid supercapacitor", Appl. Surf. Sci., 526, 146696. https://doi.org/10.1016/j.apsusc.2020.146696.
  67. Zhu, W., Deng, M., Chen, D., Zhang, Z., Chai, W., Chen, D. and Hao, Y. (2020), "Dual-phase CsPbCl3-Cs4PbCl6 perovskite films for self-powered, visible-blind UV photodetectors with fast response", ACS Appl. Mater. Interfac., 12(29), 32961-32969. https://doi.org/10.1021/acsami.0c09910.