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DOI QR Code

Wave propagation in double nano-beams in thermal environments using the Reddy's high-order shear deformation theory

  • Fei Wu (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • 투고 : 2021.06.06
  • 심사 : 2022.12.22
  • 발행 : 2023.06.25

초록

We study the bending wave, shear wave and longitudinal wave characteristics in the double nanobeams in this paper for the first time, in the process of research, based on the Reddy's higher-order shear deformation theory and considering shear layer stiffness, linear stiffness, inter-laminar stiffness, the pore volume fraction, temperature variation, functionally graded index influence on wave propagation, based on the nonlocal strain gradient theory and Hamilton variational principle, the wave equation of the double-nanometer beams are derived. Since there are three different motion states for the double nanobeams, which includes the cases of "in phase", "out of phase" and "one nanobeam fixed", the propagation characteristics of shear-, bending-, and longitudinal- waves in these three cases are discussed respectively, and some valuable conclusions are obtained.

키워드

과제정보

The authors acknowledge this work is supported by the first-rate talent introduction project of Chongqing University (02090011044159).

참고문헌

  1. Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: A micromechanical approach", Iran. J. Sci. Technol., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y
  2. Abdelrahman, A.A., Esen, I., Ozarpa, C. and Eltaher, M. A. (2021), "Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory", Appl. Math. Modell., 96, 215-235. https://doi.org/10.1016/j.apm.2021.03.008
  3. Abo-Bakr, R.M., Eltaher, M.A. and Attia, M.A. (2022), "Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects", Eng. Comput., 38(1), 255-276. https://doi.org/10.1007/s00366-020-01146-0
  4. Ahmed, H., Mohamed, Z., Khaled, B. and Tayeb, B. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
  5. Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
  6. Akgoz, B. and Civalek, O. (2015), "A novel microstructure-dependent shear deformable beam model", Int. J. Mech. Sci., 99, 10-20. https://doi.org/10.1016/j.ijmecsci.2015.05.003
  7. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35(4), 555-566. https://doi.org/10.12989/scs.2020.35.4.555
  8. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. https://doi.org/10.12989/gae.2021.24.1.091
  9. Bahaadini, R., Hosseini, M. and Khalili-Parizi, Z. (2019), "Electromechanical stability analysis of smart double-nanobeam systems", Euro. Phys. J. Plus, 134(7), 320. https://doi.org/10.1140/epjp/i2019-12644-8
  10. Barati, M. and Shahverdi, H. (2017), "Hygro-thermal vibration analysis of graded double-refined-nanoplate systems using hybrid nonlocal stress-strain gradient theory", Compos. Struct., 176, 982-995. https://doi.org/10.1016/j.compstruct.2017.06.004
  11. Barati, M. and Zenkour, A. (2017), "A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate", Compos. Struct., 168, 885-892. https://doi.org/10.1016/j.compstruct.2017.02.090
  12. Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical buckling load of triple-walled carbon nanotube based on nonlocal elasticity theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/jnanor.62.108
  13. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
  14. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircr. Spacecr. Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001
  15. Bouhadra, A., Menasria, A. and Rachedi, M.A. (2021), "Boundary conditions effect for buckling analysis of porous functionally graded nanobeam", Adv. Nano. Res., 10(4), 313-325. https://doi.org/10.12989/anr.2021.10.4.313
  16. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus, 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0
  17. Civalek, O., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method Appl. Sci., Special Issue Paper. https://doi.org/10.1002/mma.7069
  18. Civalek, O., Uzun, B. and Yayli, M.O. (2020), "Frequency, bending and buckling loads of nanobeams with different cross sections", Adv. Nano. Res., 9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091
  19. Dai, H. and Safarpour, H. (2021), "Frequency and thermal buckling information of laminated composite doubly curved open nanoshell", Adv. Nano. Res., 10(1), 1-14. https://doi.org/10.12989/anr.2021.10.1.001
  20. Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano. Res., 10(2), 175-189. https://doi.org/110.12989/anr.2021.10.2.175
  21. Daikh, A.A., Houari, M.S.A. and Eltaher, M.A. (2021a), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347
  22. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021b), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", applied sciences, 11(7), 3250. https://doi.org/10.3390/app11073250
  23. Dastjerdi, S., Akgoz, B. and Civalek, O. (2020), "On the effect of viscoelasticity on behavior of gyroscopes", Int. J. Eng. Sci., 149, 103236. https://doi.org/10.1016/j.ijengsci.2020.103236
  24. Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016
  25. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://doi.org/10.12989/sem.2021.80.1.063
  26. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  27. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concr., 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433
  28. Ebrahimi, F., Barati, M.R. and Civalek, O. (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366-019-00742-z
  29. Ebrahimi, F. and Dabbagh, A. (2018a), "NSGT-based acoustical wave dispersion characteristics of thermo-magnetically actuated double-nanobeam systems", Struct. Eng. Sci., 68(6), 701-711. https://doi.org/10.12989/sem.2018.68.6.701
  30. Ebrahimi, F. and Dabbagh, A. (2018b), "Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems", Struct. Eng. Sci., 67(2), 175-183. https://doi.org/10.12989/sem.2018.67.2.175
  31. Ebrahimi, F., Dabbagh, A. (2021), "Magnetic field effects on thermally affected propagation of acoustical waves in rotary double-nanobeam systems", Wave Random Complex, 31(1), 25-45. https://doi.org/10.1080/17455030.2018.1558308
  32. Eyvazian, A., Zhang, C., Musharavati, F., Khan, A. and Mohamed, A.M. (2021), "Elastic wave phenomenon of nanobeams including thickness stretching effect", Adv. Nano. Res., 10(3), 271-280. https://doi.org/10.12989/anr.2021.10.3.271
  33. Eringen, A.C. (1998), "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
  34. Esmaeilzadeh, M., Golmakani, M.E., Kadkhodayan, M., Amoozgar, M. and Bodaghi, M. (2021), "Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates", Adv. Nano. Res., 10(2), 151-163. https://doi.org/110.12989/anr.2021.10.2.151
  35. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38 (4), 3463-3482. https://doi.org/10.1007/s00366-021-01389-5
  36. Esen, I., Daikh, A.A. and Eltaher, M.A. (2022b), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136(4),1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7
  37. Fenjan, R.M., Moustafa, N.M., Faleh, N.M. (2020), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano. Res., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283
  38. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano. Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
  39. Ghafarian, M., Shirinzadeh, B. and Wei, W.C. (2020), "Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam", Microsyst. Technol., 26(12), 3657-3676. https://doi.org/10.1007/s00542-020-04837-2
  40. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115
  41. Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano. Res., 10(3), 281-293. https://doi.org/10.12989/anr.2021.10.3.281
  42. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089
  43. Khosravi, F., Simyari, M., Hosseini, S.A. and Tounsi, A. (2020), "Size dependent axial free and forced vibration of carbon nanotube via different rod models", Adv. Nano. Res., 9(3), 157-172. https://doi.org/10.12989/anr.2020.9.3.157
  44. Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013
  45. Jazi, S.H. (2020), "Nonlinear vibration of an elastically connected double Timoshenko nanobeam system carrying a moving particle based on modified couple stress theory", Arch. Appl. Mech., 90(12), 2739-2754. https://doi.org/10.1007/s00419-020-01746-8
  46. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  47. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428
  48. Malikan, M. and Eremeyev, V.A. (2020), "A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition", Compos. Struct., 249, 112486. https://doi.org/10.1016/j.compstruct.2020.112486.
  49. Malikan, M. and Eremeyev, V.A. (2022), "The effect of shear deformations' rotary inertia on the vibrating response of multi-physic composite beam-like actuators", Compos. Struct., 297, 115951. https://doi.org/10.1016/j.compstruct.2022.115951
  50. Malikan, M., Tornabene, F. and Dimitri, R. (2019), "Transient response of oscillated carbon nanotubes with an internal and external damping", Compos. Part B Eng., 158, 198-205. https://doi.org/10.1016/j.compositesb.2018.09.092
  51. Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2022), "Thermal buckling of functionally graded piezomagnetic micro-and nanobeams presenting the flexomagnetic effect", Continuum Mech. Thermodyn., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8
  52. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E. A. A., Tounsi, A., Mahmoud, S. R., Tounsi, A. and Benrahou, K. H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano. Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293
  53. Mousavi, S., Amir, S., Jafari, A. and Arshid, E. (2021), "Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories", Adv. Nano. Res., 10(3), 235-251. https://doi.org/10.12989/anr.2021.10.3.235
  54. Rahmani, O., Hosseini, S.A.H. and Parhizkari, M. (2017), "Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: A analytical approach", Microsyst. Technol., 23(7), 2739-2751. https://doi.org/10.1007/s00542-016-3127-5
  55. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  56. Safari, M., Mohammadimehr, M. and Ashrafi, H. (2021), "Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC", Adv. Nano. Res., 10(2),115-128. https://doi.org/10.12989/anr2021.10.2.115
  57. Salami, S.J., Boroujerdy, M.S. and Bazzaz, E. (2021), "Geometrically nonlinear thermo-mechanical bending analysis of deep cylindrical composite panels reinforced by functionally graded CNTs", Adv. Nano. Res., 10(4), 385-395. https://doi.org/10.12989/anr.2021.10.4.385
  58. Shariati, A., Ebrahimi, F., Karimiasl, M., Selvamani, R. and Toghroli, A. (2020), "On bending characteristics of smart magneto-electro-piezoelectric nanobeams system", Adv. Nano. Res., 9(3), 183-191. https://doi.org/10.12989/anr.2020.9.3.183
  59. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323
  60. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x
  61. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225
  62. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615
  63. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407
  64. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  65. Singh, P.P. Azam, M.S. (2021), "Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method", Adv. Nano. Res., 10(1), 25-42. https://doi.org/10.12989/anr.2021.10.1.025
  66. Tayeb, B., Mohamed, Z., Tahar, H.D. and Khaled, B. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
  67. Timesli, A. (2020), "Buckling analysis of double walled carbon nanotubes embedded in Kerr elastic medium under axial compression using the nonlocal Donnell shell theory", Adv. Nano. Res., 9(2), 69-82. https://doi.org/110.12989/anr.2020.9.2.069
  68. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  69. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  70. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397
  71. Zhang, Y.W., She, G.L. and Ding, H.X. (2023), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A Solids, 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887
  72. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293
  73. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797
  74. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://10.12989/anr.2022.13.5.465
  75. Zhou, Z., Li, Y. and Fan, J. (2018), "Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method", Physica E, 99, 220-235. https://doi.org/10.1016/j.physe.2018.02.003