Structural Engineering and Mechanics

  • 제76권4호
  • /
  • Pages.551-559
  • /
  • 2020
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Propagation characteristics of longitudinal wave, shear wave and bending wave in porous circular nanoplates

  • Shan, Wubin (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Deng, Zulu (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Zhong, Hao (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Mo, Hu (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Han, Ziqiang (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Yang, Zhi (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Xiang, Chengyu (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Li, Shuzhou (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Liu, Peng (School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology)
  • 투고 : 2020.05.19
  • 심사 : 2020.11.17
  • 발행 : 2020.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

On the basis of nonlocal strain gradient theory, considering the material properties of porous FGM changing with thickness and the influence of moment of inertia, the wave equation of FG nano circular plate is derived by using the first-order shear deformation plate theory, by introducing dimensionless parameters, we transform the equations into dimensionless wave equations, and the dispersion relations of bending wave, shear wave and longitudinal wave are obtained by Laplace and Hankel integral transformation method. The influence of nonlocal parameter, porosity volume fraction, strain gradient parameters and power law index on the propagation characteristics of bending wave, shear wave and longitudinal wave in FG nano circular plate.

키워드

과제정보

This paper is funded by Natural Science Foundation of Hunan Province (No. 2020JJ7020).

참고문헌

  1. Aifantis, E.C. (1992), "On the role of gradients in the localization of deformation and fracture", Int. J. Eng. Sci., 30, 1279-1299. https://doi.org/10.1016/0020-7225(92)90141-3
  2. Agwa, M. A. and Eltaher, M. A. (2016), "Vibration of a carbyne nanomechanical mass sensor with surface effect", Appl. Phys. A, 122, 335. https://doi.org/10.1007/s00339-016-9934-9
  3. Akgoz, B. and Civalek, O. (2017a), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.039
  4. Akgoz, B. and Civalek, O. (2017b), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024
  5. Arefi, M. (2016), "Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage", Appl. Math. Mech. (English Edition), 37(3), 289-302. https://doi.org/10.1007/s10483-016-2039-6
  6. Arefi, M. and Zenkour, A.M. (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
  7. Arefi, M., and Zenkour, A. M. (2016), "Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory", Mater. Res. Express, 3(11), 115704. https://doi.org/10.1088/2053-1591/3/11/115704
  8. Aria, A.I. and Biglari, H. (2018), "Computational vibration and buckling analysis of microtubule bundles based on nonlocal strain gradient theory", Appl. Math. Comput., 321, 313-332. https://doi.org/10.1016/j.amc.2017.10.050
  9. Barati, M.R. (2017), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11. https://doi.org/10.1016/j.ijengsci.2017.03.007.
  10. Barati, M.R., 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., 68, 885-892. https://doi.org/10.1016/j.compstruct.2017.02.090
  11. Ebrahimi, F. and Barati, M. R. (2016a), "Wave propagation analysis of quasi-3d fg nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1
  12. Ebrahimi, F., and Barati, M. R. (2016b), "Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field", J. Therm. Stress., 40(4-6), 1-16. https://doi.org/10.1080/01495739.2016.1254076
  13. Ebrahimi, F., and Barati, M. R. (2016c), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", App. Phys. A, 122(4), 451. https://doi.org/10.1007/s00339-016-0001-3
  14. Ebrahimi, F., and Barati, M. R. (2016d), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122, 451. https://doi.org/10.1007/s00339-016-0001-3
  15. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  16. Ebrahimi, F. and Barati, M.R. (2017b), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  17. Ebrahimi, F. and Barati, M.R. (2017c), "Flexural wave propagation analysis of embedded s-fgm nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 42(5), 1715-1726. https://doi.org/10.1007/s13369-016-2266-4
  18. Ebrahimi, F., Barati, M. R., and Haghi, P. (2017a), "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory", J. Vib. Control, 24(17), 3809-3818. https://doi.org/10.1177/1077546317711537
  19. Ebrahimi, F., Barati, M. R., and Haghi, P. (2017b), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stresses, 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  20. Ebrahimi, F., Barati, M. R., and Haghi, P. (2016), "Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams", Euro. Phys. J. Plus, 131(11), 383. https://doi.org/10.1140/epjp/i2016-16383-0.
  21. Ebrahimi, F., Barati, M.R., and Dabbagh, A. (2016a), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci., 107, 169-182.https://doi.org/10.1016/j.ijengsci.2016.07.008
  22. Ebrahimi, F. , Barati, M. R. and Dabbagh, A. (2016b), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci.,107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  23. Ebrahimi, F. and Dabbagh, A. (2017a), "Wave propagation analysis of smart rotating porous heterogeneous piezo-electric nanobeams", Euro. Phys. J. Plus, 132(4), 153. https://doi.org/10.1140/epjp/i2017-11366-3
  24. Ebrahimi, F. , and Dabbagh, A. (2017b), "Nonlocal strain gradient based wave dispersion behavior of rotating magneto-electro-elastic nanoplates", Mater. Res. Express, 4(2), 025003. https://doi.org/10.1088/2053-1591/aa55b5
  25. Ebrahimi, F., and Dabbagh, A. (2017c), "On flexural wave propagation responses of smart fg magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293. https://doi.org/10.1016/j.compstruct.2016.11.058
  26. Ebrahimi, F. , and Dabbagh, A. (2017d), "Nonlocal strain gradient based wave dispersion behavior of rotating magneto-electro-elastic nanoplates", Mater. Res. Express, 4(2), 025003. https://doi.org/10.1088/2053-1591/aa55b5
  27. Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of orthotropic double-nanoplate-system subjected to a longitudinal magnetic field", Microsyst. Technol., 24(7), 2929-2939. https://doi.org/10.1007/s00542-018-3738-0.
  28. Ebrahimi, F. , Dabbagh, A. , and Barati, M. R. (2016), "Wave propagation analysis of a size-dependent magneto-electro-elastic heterogeneous nanoplate", Euro. Phys. J. Plus, 131(12), 433. https://doi.org/10.1140/epjp/i2016-16433-7
  29. Ebrahimi, F. and Haghi, P. (2017), "Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory", Acta Mech. Solida Sin., 30(6), 647-657. https://doi.org/10.1016/j.camss.2017.09.007
  30. Ebrahimi, F., and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mechanics of Composite Materials & Structures, 24(10), 820-829. https://doi.org/10.1080/15376494.2016.1196786.
  31. Ebrahimi, F., and Shafiei, N. (2016), "Application of eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  32. Ebrahimi, F., Salari, E., and Hosseini, S. A. H. (2015), "Thermomechanical vibration behavior of fg nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  33. Ebrahimi, F., and Salari, E. (2015a), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  34. Ebrahimi, F., and Salari, E. (2015b), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES-Comp. Model. Eng., 105(2), 151-181. https://doi.org/10.3970/cmes.2015.105.151
  35. Eltaher, M.A., El-Borgi S. and Reddy J.N. (2016), "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013
  36. 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
  37. Eltaher, M.A., Attia, M.A., Soliman, A.E. and Alshorbagy, A.E. (2018), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., Int. J., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097
  38. Eltaher, M.A. and Mohamed, N. (2020a), "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
  39. Eltaher, M.A. and Mohamed, N.A. (2020b), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart. Struct. Syst., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501.
  40. Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res.Sw, 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136 .
  41. Eltaher, M. A., Almalki, T. A., Almitani, K. H., Ahmed, K. I. E., and Abdraboh, A. M. (2019), "Modal participation of fixed-fixed single-walled carbon nanotube with vacancies", J. Adv. Struct. Eng., 11, 151-163. https://doi.org/10.1007/s40091-019-0222-8.
  42. Eltaher, M. A., Omar, F. A., Abdalla, W. S. and Gad, E. H. (2019), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Wave. Random Complex, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693
  43. Eltaher, M. A., Mahmoud, F. F., Assie, A. E., and Meletis, E. I. (2013), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774. https://doi.org/10.1016/j.amc.2013.09.002.
  44. Emam, S.A., Eltaher, M.A., Khater, M.E., and Abdalla, W.S (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci.-Basel, 8(11), 2238. https://doi.org/10.3390/app8112238.
  45. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S., and Alshorbagy, A.E. (2020), "Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts", Smart. Struct. Syst., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219.
  46. Eltaher, M.A., Hamed, M.A., Sadoun, A.M., Mansour, A.A. (2014) "Mechanical analysis of higher order gradient nanobeams", Appl. Math. Comput., 229, 260-272. https://doi.org/10.1016/j.amc.2013.12.076.
  47. Eltaher, M. A., Fouda, N. , El-Midany, T. , and Sadoun, A. M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Braz. Soc. Mech. Sci., 40(3), 141. https://doi.org/10.1007/s40430-018-1065-0.
  48. 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.
  49. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  50. Faleh, N.M., Fenjan, R.M., and Ahmed, R.A. (2018), "Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads", Euro. Phys. J. Plus, 133(9), 348. https://doi.org/10.1140/epjp/i2018-12152-5
  51. Faroughi, S., Rahmani, A., and Friswell, M.I. (2020), "On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model", Appl. Math. Model., 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040
  52. Ghayesh, M.H., Farokhi, H., Gholipour, A. and Tavallaeinejad, M. (2018), "Nonlinear oscillations of functionally graded microplates", Int. J. Eng. Sci., 122, 56-72. https://doi.org/10.1016/j.ijengsci.2017.03.014
  53. Ghayesh, M.H., Farokhi, H., and Farajpour, A. (2019), "Chaos in fluid-conveying NSGT nanotubes with geometric imperfections", Appl. Math. Model., 74, 708-730. https://doi.org/10.1016/j.apm.2019.04.053
  54. 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.
  55. Hamed, M.A., Eltaher, M.A., Sadoun, A.M., and Almitani, K. H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A-Mater., 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0
  56. 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
  57. Hamed, M. A., Abo-Bakr, R. M., Mohamed, S. A. , and Eltaher, M. A. (2020), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 36(4),1929-1946. https://doi.org/10.1007/s00366-020-01023-w
  58. Li, A., Ji, X., Zhou, S.S., Wang, L., Chen, J., and Liu, P.B. (2020), "Nonlinear axisymmetric bending analysis of strain gradient thin circular plate", Appl. Math. Model., 89, 363-380. https://doi.org/10.1016/j.apm.2020.08.004
  59. Malikan, M. and Nguyen, V.B. (2018), "Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory", Physica E, 102, 8-28. https://doi.org/10.1016/j.physe.2018.04.018
  60. Malikan, M., Nguyen, V.B. and Tornabene, F. (2018), "Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory", Mater. Res. Express,5(75031), 1-20. https://doi.org/10.1088/2053-1591/aad144.
  61. Malikan, M., Krasheninnikov, M., and Eremeyev, M.V. (2020), "Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field", Int. J. Eng. Sci., 148, 103210. https://doi.org/10.1016/j.ijengsci.2019.103210
  62. Melaibari, A., Abo-Bakr, R. M. , Mohamed, S. A. , and Eltaher, M. A. (2020), "Static stability of higher order functionally graded beam under variable axial load", Alex. Eng. J., 59(3), 1661-1675. https://doi.org/10.1016/j.aej.2020.04.012
  63. Melaibari, A., Khoshaim, A.B., Mohamed, S.A., and Eltaher, M.A. (2020), "Static stability and of symmetric and sigmoid functionally graded beam under variable axial load", Steel Compos. Struct., 35(5), 671-685. https://doi.org/10.12989/scs.2020.35.5.671
  64. Mindlin, R.D. (1965), "Second gradient of strain and surface-tension in linear elasticity", Int. J. Solid Struct., 1(4), 417-438. https://doi.org/10.1016/0020-7683(65)90006-5.
  65. Sun, D. and Luo, S.N. (2012), "Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments", Appl. Math. Model., 36(1), 444-462. https://doi.org/10.1016/j.apm.2011.07.023
  66. Zhang, H., Wang, C.M., Challamel, N, and Pan, W.H. (2020), "Calibration of Eringen's small length scale coefficient for buckling circular and annular plates via Hencky bar-net model", Appl. Math. Model., 78, 399-417. https://doi.org/10.1016/j.apm.2019.09.052
  67. Zhu, F., Pan E, Qian Z, and Wang Y. (2019), "Dispersion curves, mode shapes, stresses and energies of SH and Lamb waves in layered elastic nanoplates with surface/interface effect", Int. J. Eng. Sci., 142,170-184. https://doi.org/10.1016/j.ijengsci.2019.06.003
  68. Zur, K.K. (2019), "Free vibration analysis of discrete-continuous functionally graded circular plate via the Neumann series method", Appl. Math. Model., 73, 166-189. https://doi.org/10.1016/j.apm.2019.02.047