Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Small-scale effects on wave propagation in curved nanobeams subjected to thermal loadings based on NSGT

  • Ibrahim Ghoytasi (Department of Mechanical Engineering, Sharif University of Technology) ;
  • Reza Naghdabadi (Department of Mechanical Engineering, Sharif University of Technology)
  • Received : 2023.03.26
  • Accepted : 2023.12.14
  • Published : 2024.02.25
⟨ Previous Next ⟩

Abstract

This study focuses on wave propagation analysis in the curved nanobeam exposed to different thermal loadings based on the Nonlocal Strain Gradient Theory (NSGT). Mechanical properties of the constitutive materials are assumed to be temperature-dependent and functionally graded. For modeling, the governing equations are derived using Hamilton's principle. Using the proposed model, the effects of small-scale, geometrical, and thermo-mechanical parameters on the dynamic behavior of the curved nanobeam are studied. A small-scale parameter, Z, is taken into account that collectively represents the strain gradient and the nonlocal parameters. When Z<1 or Z>1, the phase velocity decreases/increases, and the stiffness-softening/hardening phenomenon occurs in the curved nanobeam. Accordingly, the phase velocity depends more on the strain gradient parameter rather than the nonlocal parameter. As the arc angle increases, more variations in the phase velocity emerge in small wavenumbers. Furthermore, an increase of ∆T causes a decrease in the phase velocity, mostly in the case of uniform temperature rise rather than heat conduction. For verification, the results are compared with those available for the straight nanobeam in the previous studies. It is believed that the findings will be helpful for different applications of curved nanostructures used in nano-devices.

Keywords

Acknowledgement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-forprofit sectors.

References

  1. Akgoz, B. and O . Civalek (2013), "Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)", Compos. Part B Eng., 55, 263-268. https://doi.org/10.1016/j.compositesb.2013.06.035.
  2. Al-Furjan, M., M.A. Oyarhossein, M. Habibi, H. Safarpour, D.W. Jung and A. Tounsi (2021), "On the wave propagation of the multi-scale hybrid nanocomposite doubly curved viscoelastic panel", Compos. Struct., 255, 112947. https://doi.org/10.1016/j.compstruct.2020.112947.
  3. Alazwari, M.A., I. Esen, A.A. Abdelrahman, A.M. Abdraboh and M.A. Eltaher (2022), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermomagnetic fields and moving load", Adv. Nano Res., 12(3), 231-251. https://doi.org/10.12989/anr.2022.12.3.231.
  4. Alwabli, A.S., A. Kaci, H. Bellifa, A.A. Bousahla, A. Tounsi, D.A. Alzahrani, A.A. Abulfaraj, F. Bourada, K.H. Benrahou and A. Tounsi (2021), "The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory", Adv. Nano Res., 10(1), 15-24. https://doi.org/10.12989/anr.2021.10.1.015.
  5. Arefi, M. and A.M. Zenkour (2017), "Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation", Mech. Res. Commun., 79, 51-62. https://doi.org/10.1016/j.mechrescom.2017.01.004.
  6. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  7. Barretta, R., F.M. de Sciarra and M.S. Vaccaro (2019), "On nonlocal mechanics of curved elastic beams", Int. Eng. Sci., 144, 103140. https://doi.org/10.1016/j.ijengsci.2019.103140.
  8. Bensaid, I., A. Bekhadda and B. Kerboua (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279. https://doi.org/10.12989/anr.2018.6.3.279.
  9. Boyina, K. and R. Piska (2023), "Wave propagation analysis in viscoelastic Timoshenko nanobeams under surface and magnetic field effects based on nonlocal strain gradient theory", Appl. Math. Comput., 439, 127580. https://doi.org/10.1016/j.amc.2022.127580.
  10. Carbonari, R.C., E.C. Silva and G.H. Paulino (2009), "Multi-actuated functionally graded piezoelectric micro-tools design: A multiphysics topology optimization approach", Int. J. Numer. Meth. Eng., 77(3), 301-336. https://doi.org/10.1002/nme.2403.
  11. Ebrahimi, F., A. Dabbagh, T. Rabczuk and F. Tornabene (2019a), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porositydependent homogenization scheme", Adv. Nano Res., 7(2), 135. https://doi.org/10.12989/anr.2019.7.2.135.
  12. Ebrahimi, F., A. Seyfi and A. Dabbagh (2019b), "Dispersion of waves in FG porous nanoscale plates based on NSGT in thermal environment", Adv. Nano Res., 7(5), 325-335. https://doi.org/10.12989/anr.2019.7.5.325.
  13. Eltaher, M., M. Khater and S.A. Emam (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Modell., 40, 5-6, 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  14. 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.
  15. Faroughi, S., A. Rahmani and M. Friswell (2020), "On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model", Appl. Math. Modell., 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040.
  16. Ganapathi, M. and O. Polit (2018), "A nonlocal higher-order model including thickness stretching effect for bending and buckling of curved nanobeams", Appl. Math. Modell., 57, 121-141. https://doi.org/10.1016/j.apm.2017.12.025.
  17. Ghandourah, E.E., H.M. Ahmed, M.A. Eltaher, M.A. Attia and A.M. Abdraboh (2021), "Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model", Adv. Nano Res., 11(4), 405-422. https://doi.org/10.12989/anr.2021.11.4.405.
  18. Ghayesh, M.H. and A. Farajpour (2019), "A review on the mechanics of functionally graded nanoscale and microscale structures", Int. Eng. Sci., 137, 8-36. https://doi.org/10.1016/j.ijengsci.2018.12.001.
  19. Gorgani, H.H., M.M. Adeli and M. Hosseini (2019), "Pull-in behavior of functionally graded micro/nano-beams for MEMS and NEMS switches", Microsyst. Technol., 25(8), 3165-3173. https://doi.org/10.1007/s00542-018-4216-4.
  20. Hadji, L. and M. Avcar (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.
  21. Hashemian, A. and S.F. Hosseini (2019), "Nonlinear bifurcation analysis of statically loaded free-form curved beams using isogeometric framework and pseudo-arclength continuation", Int. J. Non-Linear Mech., 113, 1-16. https://doi.org/10.1016/j.ijnonlinmec.2019.03.002.
  22. Hu, T., W. Yang, X. Liang and S. Shen (2018), "Wave propagation in flexoelectric microstructured solids", J. Elast., 130, 2, 197-210. https://doi.org/10.1007/s10659-017-9636-3.
  23. Kiani, K. (2016), "Thermo-elasto-dynamic analysis of axially functionally graded non-uniform nanobeams with surface energy", Int. Eng. Sci., 106, 57-76. https://doi.org/10.1016/j.ijengsci.2016.05.004.
  24. Kiani, Y., M. Rezaei, S. Taheri and M. Eslami (2011), "Thermoelectrical buckling of piezoelectric functionally graded material Timoshenko beams", Int. J. Mech. Mater. Des., 7(3), 185-197. https://doi.org/10.1007/s10999-011-9158-2.
  25. Komeili, A., A.H. Akbarzadeh, A. Doroushi and M.R. Eslami (2011), "Static analysis of functionally graded piezoelectric beams under thermo-electro-mechanical loads", Adv. Mech. Eng., 3, 153731. https://doi.org/10.1155/2011/153731.
  26. Komijani, M., S. Esfahani, J. Reddy, Y. Liu and M. Eslami (2014), "Nonlinear thermal stability and vibration of pre/postbuckled temperature-and microstructure-dependent functionally graded beams resting on elastic foundation", Compos. Struct., 112, 292-307. https://doi.org/10.1016/j.compstruct.2014.01.041.
  27. Komijani, M., Y. Kiani, S. Esfahani and M. Eslami (2013), "Vibration of thermo-electrically post-buckled rectangular functionally graded piezoelectric beams", Compos. Struct., 98, 143-152. https://doi.org/10.1016/j.compstruct.2012.10.047.
  28. Lai, W.M., D.H. Rubin, D. Rubin and E. Krempl (2009), Introduction to Continuum Mechanics, Butterworth-Heinemann.
  29. Lam, D.C., F. Yang, A. Chong, J. Wang and P. Tong (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  30. Li, C., C. Zhu, N. Zhang, S. Sui and J. Zhao (2022), "Free vibration of self-powered nanoribbons subjected to thermalmechanical-electrical fields based on a nonlocal strain gradient theory", Appl. Math. Modell., 110, 583-602. https://doi.org/10.1016/j.apm.2022.05.044,
  31. Li, L., Y. Hu and L. Ling (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014.
  32. Lim, C., G. Zhang and J. Reddy (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.
  33. Liu, Y. and J. Reddy (2011), "A nonlocal curved beam model based on a modified couple stress theory", Int. J. Struct. Stabil. Dyn., 11(3), 495-512. https://doi.org/10.1142/S0219455411004233.
  34. Lu, L., X. Guo and J. Zhao (2017), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. Eng. Sci., 116, 12-24. https://doi.org/10.1016/j.ijengsci.2017.03.006.
  35. Ma, L.H., L.L. Ke, Y.Z. Wang and Y.S. Wang (2017), "Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models", Physica E, 86, 253-261. https://doi.org/10.1016/j.physe.2016.10.036.
  36. Matouk, H., A.A. Bousahla, H. Heireche, F. Bourada, E. Bedia, A. Tounsi, S. Mahmoud, A. Tounsi and K. Benrahou (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.
  37. Miller, R.E. and V.B. Shenoy (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11(3), 139. http://doi.org/10.1088/0957-4484/11/3/301.
  38. Mindlin, R.D. (1965), "Second gradient of strain and surfacetension in linear elasticity", Int. J. Solids Struct., 1(4), 417-438. https://doi.org/10.1016/0020-7683(65)90006-5.
  39. Mohammadimehr, M., M. Farahi and S. Alimirzaei (2016), "Vibration and wave propagation analysis of twisted microbeam using strain gradient theory", Appl. Math. Mech., 37(10), 1375-1392. https://doi.org/10.1007/s10483-016-2138-9.
  40. Nanda, N. and S. Kapuria (2015), "Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories", Compos. Struct., 132, 310-320. https://doi.org/10.1016/j.compstruct.2015.04.061.
  41. Numanoglu, H.M. and O. Civalek (2019), "On the dynamics of small-sized structures", Int. Eng. Sci., 145, 103164. https://doi.org/10.1016/j.ijengsci.2019.103164.
  42. Papargyri-Beskou, S., D. Polyzos and D. Beskos (2009), "Wave dispersion in gradient elastic solids and structures: a unified treatment", Int. J. Solids Struct., 46(21), 3751-3759. https://doi.org/10.1016/j.ijsolstr.2009.05.002.
  43. Rahaeifard, M., M. Kahrobaiyan and M. Ahmadian (2010), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers And Information In Engineering Conference, American Society of Mechanical Engineers Digital Collection. https://doi.org/10.1115/DETC2009-86254.
  44. Rahmani, O., S. Hosseini, I. Ghoytasi and H. Golmohammadi (2017), "Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties", Appl. Phys. A, 123(1), 4. https://doi.org/10.1007/s00339-016-0591-9.
  45. Rahmani, O., S. Hosseini, I. Ghoytasi and H. Golmohammadi (2018), "Free vibration of deep curved FG nano-beam based on modified couple stress theory", Steel Compos. Struct., 26(5), 607-620. https://doi.org/10.12989/scs.2018.26.5.607.
  46. Reddy, J. and C. Chin (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165.
  47. Sadeghi, H., M. Baghani and R. Naghdabadi (2012), "Strain gradient elasticity solution for functionally graded microcylinders", Int. Eng. Sci., 50(1), 22-30. https://doi.org/10.1016/j.ijengsci.2011.09.006.
  48. Shabana, Y.M., M.A. Samy, M.A. Abdel-Aziz, M.E. Hindawi, M.G. Mosry, A.R.M. Albarawy, M.M. Omar, A.A. Mohamed and A.A. Attia (2021), "Enhancing the performance of microbiosensors by functionally graded geometrical and material parameters", Arch. Appl. Mech., 91(6), 2497-2511. https://doi.org/10.1007/s00419-021-01900-w.
  49. Shahsavari, D., B. Karami and A. Tounsi (2023), "Wave propagation in a porous functionally graded curved viscoelastic nano-size beam", Wave Random Complex Med., 1-22. https://doi.org/10.1080/17455030.2022.2164376.
  50. She, G.L., F.G. Yuan and Y.R. Ren (2018), "On wave propagation of porous nanotubes", Int. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002.
  51. Shen, H.S. (2016), Functionally graded materials: nonlinear analysis of plates and shells, CRC press.
  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. Timoshenko, S. P. (1922), "X. On the transverse vibrations of bars of uniform cross-section", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43, 253, 125-131. https://doi.org/10.1080/14786442208633855.
  54. Tlidji, Y., R. Benferhat, T.H. Daouadji, A. Tounsi and L.C. Trinh (2022), "Free vibration analysis of FGP nanobeams with classical and non-classical boundary conditions using Statespace approach", Adv. Nano Res., 13(5), 453-463. https://doi.org/10.12989/anr.2022.13.5.453.
  55. Wang, X., X. Ren, H. Zhou, J. Yu and K. Li (2023), "Dynamics of thermoelastic Lamb waves in functionally graded nanoplates based on the modified nonlocal theory", Appl. Math. Modell., 117, 142-161. https://doi.org/10.1016/j.apm.2022.12.022.
  56. Xing, L., W. Liu, X. Li, H. Wang, Z. Jiang and L. Wang (2022), "Application of machine learning and deep neural network for wave propagation in lung cancer cell", Adv. Nano Res., 13(3), 297-312. https://doi.org/10.12989/anr.2022.13.3.297.
  57. Xu, F., Q. Qin, A. Mishra, Y. Gu and Y. Zhu (2010), "Mechanical properties of ZnO nanowires under different loading modes", Nano Res., 3(4), 271-280. https://doi.org/10.1007/s12274-010-1030-4.
  58. Yan, Z. and L. Jiang (2011), "Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects", J. Phys. D Appl. Phys., 44(36), 365301. http://doi.org/10.1088/0022- 3727/44/36/365301.
  59. Yang, F., A. Chong, D.C.C. Lam and P. Tong (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  60. Zenkour, A.M. and M. Sobhy (2015), "A simplified shear and normal deformations nonlocal theory for bending of nanobeams in thermal environment", Physica E, 70, 121-128. https://doi.org/10.1016/j.physe.2015.02.022.
  61. Zhao, J. and Z. Yu (2021), "On the modeling and simulation of the nonlinear dynamic response of NEMS via a couple of nonlocal strain gradient theory and classical beam theory", Adv. Nano Res., 11(5), 547. https://doi.org/10.12989/anr.2021.11.5.547.