DOI QR코드

DOI QR Code

Vibrations and stress analysis of perforated functionally graded rotating beams

  • Alaa A. Abdelrahman (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Hanaa E. Abd-El-Mottaleb (Department of structural Engineering, Faculty of Engineering, Zagazig university) ;
  • Mohamed G. Elblassy (Department of structural Engineering, Faculty of Engineering, Zagazig university) ;
  • Eman A. Elshamy (Department of structural Engineering, Faculty of Engineering, Zagazig university)
  • 투고 : 2023.03.15
  • 심사 : 2023.10.10
  • 발행 : 2023.12.25

초록

In the context of finite element method, a computational simulation is presented to study and analyze the dynamic behavior of regularly perforated functionally graded rotating beam for the first time. To investigate the effect of perforation configurations, both regular circular and squared perforation patterns are studied. To explore impacts of graded material distributions, both axial and transverse gradation profiles are considered. The material characteristics of graded materials are assumed to be smoothly and continuously varied through the axial or the thickness direction according the nonlinear power gradation law. A computational finite elements procedure is presented. The accuracy of the numerical procedure is verified and compared. Resonant frequencies, axial displacements as well as internal stress distributions throughout the perforated graded rotating cantilever beam are studied. Effects of material distributions, perforation patterns, as well as the rotating beam speed are investigated. Obtained results proved that the graded material distribution has remarkable effects on the dynamic performance. Additionally, circular perforation pattern produces more softening effect compared with squared perforation configuration thus larger values of axial displacements and maximum principal stresses are detected. Moreover, squared perforation provides smaller values of nondimensional frequency parameters at most of vibration modes compared with circular pattern.

키워드

참고문헌

  1. Abdelrahman, A.A. and El-Shafei, A.G. (2021), "Modeling and analysis of the transient response of viscoelastic solids", Waves Random Complex Media, 31(6), 1990-2020. https://doi.org/10.1080/17455030.2020.1714790.
  2. Abdelrahman, A.A., Ashry, M., Alshorbagy, A.E. and Abdallah, W. S. (2021), "On the mechanical behavior of two directional symmetrical functionally graded beams under moving load", Int. J. Mech. Mater. Des., 17(3), 563-586. https://doi.org/10.1007/s10999-021-09547-9.
  3. Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendy, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  4. Abdelrahman, A.A., Nabawy, A.E., Abdelhaleem, A.M., Alieldin, S.S. and Eltaher, M.A. (2022), "Nonlinear dynamics of viscoelastic flexible structural systems by finite element method", Eng. Comput., 38(Suppl1), 169-190. https://doi.org/10.1007/s00366-020-01141-5.
  5. Abdelrahman, A.A., Abd El Mottaleb, H.E. and Eltaher, M.A. (2020), "On bending analysis of perforated microbeams including the microstructure effects", Struct. Eng. Mech., 76(6), 765-779. https://doi.org/10.12989/sem.2020.76.6.765.
  6. Akbas, S.D. (2022), "Moving-load dynamic analysis of AFG beams under thermal effect", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  7. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 1077546320947302. https://doi.org/10.1177/1077546320947302.
  8. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. https://doi.org/10.1177/1077546320947302.
  9. Alazwari, M.A., Eltaher, M.A. and Abdelrahman, A.A. (2022), "On bending of cutout nanobeams based on nonlocal strain gradient elasticity theory", Steel Compos. Struct., 43(6), 707-723. https://doi.org/10.12989/scs.2022.43.6.707.
  10. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.
  11. 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.
  12. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Influence of the perforation configuration on dynamic behaviors of multilayered beam structure", Structures, 28, 1413-1426, https://doi.org/10.1016/j.istruc.2020.09.055.
  13. Almitani, K.H., Eltaher, M., Abdelrahman, A.A. and Abd-El-Mottaleb, H.E. (2021), "Finite element based stress and vibration analysis of axially functionally graded rotating beams", Struct. Eng. Mech., 79(1), 23-33. https://doi.org/10.12989/sem.2021.79.1.023.
  14. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A.E. (2021), "Damped forced vibration analysis of layered functionally graded thick beams with porosity", Smart Struct. Syst., 27(4), 679-689. https://doi.org/10.12989/sss.2021.27.4.679.
  15. Al-Qaisia, A. (2008), "Dynamics of a rotating beam with flexible root and flexible hub", Struct. Eng. Mech., 30(4), 427-444. https://doi.org/10.12989/sem.2008.30.4.427.
  16. Amoozgar, M. and Gelman, L. (2021), "Vibration analysis of rotating porous functionally graded material beams using exact formulation", J. Vib. Control, 28(21-22), 3195-3206. https://doi.org/10.1177/10775463211027883.
  17. Arvin, H., Hosseini, S.M.H. and Kiani, Y. (2021), "Free vibration analysis of pre/post buckled rotating functionally graded beams subjected to uniform temperature rise", Thin-Wall. Struct., 158, 107187. https://doi.org/10.1016/j.tws.2020.107187.
  18. Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Dynamic analysis of layered functionally graded viscoelastic deep beams with different boundary conditions due to a pulse load", Int. J. Appl. Mech., 12(05), 2050055. https://doi.org/10.1142/S1758825120500556.
  19. Attia, M.A. and Abdelrahman, A.A. (2018), "On vibrations of functionally graded viscoelastic nanobeams with surface effects", Int. J. Eng. Sci., 127, 1-32. https://doi.org/10.1016/j.ijengsci.2018.02.005.
  20. Attia, M.A., Eltaher, M.A., Soliman, A., Abdelrahman, A.A. and Alshorbagy, A.E. (2018), "Thermoelastic crack analysis in functionally graded pipelines conveying natural gas by an FEM", Int. J. Appl. Mech., 10(04), 1850036. https://doi.org/10.1142/S1758825118500369.
  21. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  22. Bhattacharya, S. and Das, D. (2019), "Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory", Compos. Struct., 215, 471-492. https://doi.org/10.1016/j.compstruct.2019.01.080.
  23. Bhavar, V., Kattire, P., Thakare, S. and Singh, R. (2017), "A review on functionally gradient materials (FGMs) and their applications", IOP Conference Series: Materials Science and Engineering, https://doi.org/10.1088/1757-899X/229/1/012021
  24. Chhabra, P.P.S. and Ganguli, R. (2010), "Superconvergent finite element for coupled torsional-flexural-axial vibration analysis of rotating blades", Int. J. Comput. Meth. Eng. Sci. Mech., 11(1), 48-69. https://doi.org/10.1080/15502280903446838.
  25. Ebrahimi, F. and Mokhtari, M. (2014), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 37(4), 1435-1444. https://doi.org/10.1007/s40430-014-0255-7.
  26. Ebrahimi, F. and Mokhtari, M. (2015), "Semi-analytical vibration characteristics of rotating timoshenko beams made of functionally graded materials", Latin Amer. J. Solids Struct., 12(7), 1319-1339. https://doi.org/10.1590/1679-78251446.
  27. Eltaher, M.A. and Abdelrahman, A.A. (2020), "Bending behavior of squared cutout nanobeams incorporating surface stress effects", Steel Compos. Struct., 36(2), 143-161. https://doi.org/10.12989/scs.2020.36.2.143
  28. Eltaher, M.A. and Akbas, S.D. (2020), "Transient response of 2D functionally graded beam structure", Struct. Eng. Mech., 75(3), 357-367. https://doi.org/10.12989/sem.2020.75.3.357.
  29. Eltaher, M.A., Abdelmoteleb, H.E., Daikh, A.A. and Abdelrahman, A.A. (2021), "Vibrations and stress analysis of rotating perforated beams by using finite elements method", Steel Compos. Struct., 41(4), 505-520. https://doi.org/10.12989/scs.2021.41.4.505
  30. 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. Mathem. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.
  31. Esen, I. (2019), "Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass", Int. J. Mech. Sci., 153, 21-35. https://doi.org/10.1016/j.ijmecsci.2019.01.033.
  32. Esen, I. (2020), "Dynamics of size-dependant Timoshenko micro beams subjected to moving loads", Int. J. Mech. Sci., 175, 105501. https://doi.org/10.1016/j.ijmecsci.2020.105501.
  33. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021a), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17(3), 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  34. Esen, I., Eltaher, M.A. and Abdelrahman, A.A. (2021b), "Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass", Mech. Based Des. Struct. Machines, 1-25. https://doi.org/10.1080/15397734.2021.1904255.
  35. Falkowicz, K. (2022), "Stability analysis of thin-walled perforated composite columns using finite element method", Materials, 15(24), 8919. https://doi.org/10.3390/ma15248919.
  36. Falkowicz, K. (2023), "Experimental and numerical failure analysis of thin-walled composite plates using progressive failure analysis", Compos. Struct., 305, 116474. https://doi.org/10.1016/j.compstruct.2022.116474.
  37. Fang, J., Yin, B., Zhang, X. and Yang, B. (2021), "Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(6), 2756-2774. https://doi.org/10.1177/09544062211038029.
  38. Fang, J., Zhou, D. and Dong, Y. (2018), "Three-dimensional vibration of rotating functionally graded beams", J. Vib. Control, 24(15), 3292-3306. https://doi.org/10.1177/1077546317703867.
  39. Faroughi, S., Rahmani, A. and Friswell, M. (2020), "On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model", Appl. Mathem. Modelling, 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040.
  40. Farsadi, T. (2022), "Variable thickness thin-walled rotating blades made of functionally graded porous materials", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(14), 7674-7689. https://doi.org/10.1177/09544062221080654.
  41. Ghadiri, M. and Shafiei, N. (2016), "Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions", Acta Astronautica, 121, 221-240. https://doi.org/10.1016/j.actaastro.2016.01.003.
  42. Hosseini, S.M.H., Arvin, H. and Kiani, Y. (2022), "On buckling and post-buckling of rotating clamped-clamped functionally graded beams in thermal environment", Mech. Based Des. Struct. Machines, 50(8), 2779-2794. https://doi.org/10.1080/15397734.2020.1784205
  43. Kahya, V. and Turan, M. (2017), "Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 109, 108-115. https://doi.org/10.1016/j.compositesb.2016.10.039.
  44. Karamanli, A. and Aydogdu, M. (2019), "Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory", Int. J. Mech. Sci., 159, 165-181. https://doi.org/10.1016/j.ijmecsci.2019.05.047,
  45. Liu, L.T., Hao, Y.X., Zhang, W. and Chen, J. (2018), "Free vibration analysis of rotating pretwisted functionally graded sandwich blades", Int. J. Aeros. Eng., 2018, 1-18. https://doi.org/10.1155/2018/2727452.
  46. Lotfan, S., Anamagh, M.R., Bediz, B. and Cigeroglu, E. (2021), "Nonlinear resonances of axially functionally graded beams rotating with varying speed including Coriolis effects", Nonlinear Dyn., 107(1), 533-558. https://doi.org/10.1007/s11071-021-07055-1.
  47. Mahmoud, F.F., El-Shafei, A.G., Attia, M.A. and Rahman, A.A. (2013), "Analysis of quasistatic frictional contact problems in nonlinear viscoelasticity with large deformations", Int. J. Mech. Sci., 66, 109-119. https://doi.org/10.1016/j.ijmecsci.2012.11.001.
  48. Malik, P. and Kadoli, R. (2017), "Thermo-elastic response of SUS316-Al 2 O 3 functionally graded beams under various heat loads", Int. J. Mech. Sci., 128-129, 206-223. https://doi.org/10.1016/j.ijmecsci.2017.04.014.
  49. Mohanty, S., Dash, R. and Rout, T. (2013), "Free vibration of a functionally graded rotating Timoshenko beam using FEM", Adv. Struct. Eng., 16(2), 405-418. https://doi.org/10.1260/1369-4332.16.2.405.
  50. Nabawy, A.E., Abdelhaleem, A.M., Alieldin, S.S. and Abdelrahman, A.A. (2022), "Study of the dynamic behavior of porous functionally graded suspension structural systems using finite elements methods", Steel Compos. Struct., 45(5), 697-713. https://doi.org/10.12989/scs.2022.45.5.697.
  51. Nabawy, A.E., Abdelrahman, A.A., Abdalla, W.S., Abdelhaleem, A.M. and Alieldin, S.S. (2019), "Analysis of the dynamic behavior of the double wishbone suspension system", Int. J. Appl. Mech., 11(05), 1950044. https://doi.org/10.1142/S1758825119500443.
  52. Naebe, M. and Shirvanimoghaddam, K. (2016), "Functionally graded materials: A review of fabrication and properties", Appl. Mater. Today, 5, 223-245. https://doi.org/10.1016/j.apmt.2016.10.001.
  53. O zdemir, O . (2022), "Vibration and buckling analyses of rotating axially functionally graded nonuniform beams", J. Vib. Eng. Technol., 10(4), 1381-1397. https://doi.org/10.1007/s42417-022-00453-8
  54. Ozmen, R., Kilic, R. and Esen, I. (2022), "Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal fields", Mech. Adv. Mater. Struct., 1-20. https://doi.org/10.1080/15376494.2022.2124000.
  55. Pradhan, K.K. and Chakraverty, S. (2014), "Effects of different shear deformation theories on free vibration of functionally graded beams", Int. J. Mech. Sci., 82, 149-160. https://doi.org/10.1016/j.ijmecsci.2014.03.014.
  56. Rao, S.S. (2019), Vibration of Continuous systems. John Wiley & Sons.
  57. Shanab, R.A., Mohamed N.A., Eltaher, M.A., Abdelrahman, A.A. (2023), "Dynamic characteristics of viscoelastic nanobeams including cutouts", Adva. Nano Res., 14(1), 45-65. https://doi.org/10.12989/anr.2023.14.1.045.
  58. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013.
  59. 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
  60. Storch, J. and Elishakoff, I. (2017), "Vibration of functionally graded rotating beams including the effects of nonlocal elasticity", AIAA J., 55(4), 1480-1486. https://doi.org/10.2514/1.J055038.
  61. Tian, J., Zhang, Z. and Hua, H. (2019), "Free vibration analysis of rotating functionally graded double-tapered beam including porosities", Int. J. Mech. Sci., 150, 526-538. https://doi.org/10.1016/j.ijmecsci.2018.10.056.
  62. Zohra, Z., Lemya, H., Abderahman, Y., Mustapha, M., Abdelouahed, T. and Djamel, O. (2017), "Free vibration analysis of functionally graded beams using a higher-order shear deformation theory", Mathem. Modelling Eng. Prob., 4(1), 7-12. https://doi.org/10.18280/mmep.040102.