Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Waves dispersion in an imperfect functionally graded beam resting on visco-Pasternak foundation

  • Saeed I. Tahir (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Abdelbaki Chikh (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Ismail M. Mudhaffar (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mohammed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2022.09.13
  • Accepted : 2023.02.28
  • Published : 2023.05.10
⟨ Previous Next ⟩

Abstract

This article investigates the effect of viscoelastic foundations on the waves' dispersion in a beam made of ceramic-metal functionally graded material (FGM) with microstructural defects. The beam is considered to be shear deformable, and a simple three-unknown sinusoidal integral higher-order shear deformation beam theory is applied to represent the beam's displacement field. Novel to this study is the investigation of the impact of viscosity damping on imperfect FG beams, utilizing a few-unknowns theory. The stresses and strains are obtained using the two-dimensional elasticity relations of FGM, neglecting the normal strain in the beam's depth direction. The variational operation is employed to define the dispersion relations of the FGM beam. The influences of the material gradation exponent, the beam's thickness, the porosity, and visco-Pasternak foundation parameters are represented. Results showed that phase velocity was inversely proportional to the damping and porosity of the beams. Additionally, the foundation viscous damping had a stronger influence on wave velocity when porosity volume fractions were low.

Keywords

Acknowledgement

The authors would like to acknowledge the support provided by the Interdisciplinary Research Center for Construction & Building Materials (IRC-CBM) at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia, for funding this work through Project No. INCB2209. The support provided by the Department of Civil & Environmental Engineering, KFUPM, Saudi Arabia, is also greatly acknowledged.

References

  1. Adiyaman, G., Birinci, A., Oner, E. and Yaylaci, M. (2016), "A receding contact problem between a functionally graded layer and two homogeneous quarter planes", Acta Mechanica, 227(6), 1753-1766. https://doi.org/10.1007/s00707-016-1580-y.
  2. Aminipour, H. and Janghorban, M. (2017), "Wave propagation in anisotropic plates using trigonometric shear deformation theory", Mech. Adv. Mater. Struct., 24(13), 1135-1144. https://doi.org/10.1080/15376494.2016.1227500.
  3. Arani, A.G., Pourjamshidian, M., Arefi, M. and Arani, M.R.G. (2019), "Application of nonlocal elasticity theory on the wave propagation of flexoelectric functionally graded (FG) Timoshenko nano-beams considering surface effects and residual surface stress", Smart Struct. Syst., 23(2), 141-153. https://doi.org/10.12989/sss.2019.23.2.141.
  4. Benmalek, H., Salah, B. and Bouzerd, H. (2021), "Mixed finite element for the analysis of FGM beams", Int. Rev. Mech. Eng., 15(1). https://doi.org/10.15866/ireme.v15i1.19680.
  5. Birinci, A., Adiyaman, G., Yaylaci, M. and Oner, E. (2015), "Analysis of continuous and discontinuous cases of a contact problem using analytical method and FEM", Latin Am. J. Solid Struct., 12(9), 1771-1789. https://doi.org/10.1590/1679-78251574.
  6. Chen, S., Geng, R. and Li, S. (2021), "Vibration analysis of functionally graded beams using a higher-order shear deformable beam model with rational shear stress distribution", Compos. Struct., 277, 114586. https://doi.org/10.1016/j.compstruct.2021.114586.
  7. Civalek, O., Uzun, B. and Ozgur Yayli, M. (2022), "A fourier sine series solution of static and dynamic response of nano/micro-scaled FG rod under torsional effect", Adv. Nano Res., 12(5), 467-482. https://doi.org/10.12989/anr.2022.12.5.467.
  8. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porouscellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  9. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38, 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  10. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condensed Matter, 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  11. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and Nguyen-Xuan, H. (2022b), "A 3D nano scale iga for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnology, 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  12. Dai, J., Liu, Y. and Tong, G. (2022), "Wave propagation analysis of thermoelastic functionally graded nanotube conveying nanoflow", J. Vib. Control, 28(3-4), 339-350. https://doi.org/10.1177/1077546320977044.
  13. Dastjerdi, S., Malikan, M., Dimitri, R. and Tornabene, F. (2021), "Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment", Compos. Struct., 255, 112925. https://doi:10.1016/j.compstruct.2020.112925.
  14. Ebrahimi, F., Seyfi, A., Nouraei, M. and Haghi, P. (2021), "Influence of magnetic field on the wave propagation response of functionally graded (FG) beam lying on elastic foundation in thermal environment", Waves in Random and Complex Media, 1-19. https://doi:10.1080/17455030.2020.1847359.
  15. 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.
  16. Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B, 72, 1-9. https://doi:10.1016/j.compositesb.2014.12.004.
  17. Gao, W., Qin, Z. and Chu, F. (2020), "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerosp. Sci. Technol., 102. 105860. https://doi:10.1016/j.ast.2020.105860.
  18. Ghannadpour, S., Amir, M. and Khajeh, S. (2022), "Nonlinear bending and post-buckling behaviors of FG small-scaled plates based on modified strain gradient theory using ritz technique", Adv. Nano Res., 13(4), 393-406. https://doi:10.12989/anr.2022.13.4.393.
  19. Kaddari, M., Kaci, A., Anis Bousahla, A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  20. Kiarasi, F., Babaei, M., Asemi, K., Dimitri, R. and Tornabene, F. (2021), "Three-dimensional buckling analysis of functionally graded saturated porous rectangular plates under combined loading conditions", Appl. Sci., 11(21), 10434. https://doi.org/10.3390/app112110434.
  21. Koutoati, K., Mohri, F. Daya, E.M. and Carrera, E. (2021), "A finite element approach for the static and vibration analyses of functionally graded material viscoelastic sandwich beams with nonlinear material behavior", Compos. Struct., 274, 114315. https://doi.org/10.1016/j.compstruct.2021.114315.
  22. Lata, P. and Himanshi, H. (2022), "Rotational and fractional effect on Rayleigh waves in an orthotropic magneto-thermoelastic media with hall current", Steel Compos. Struct., 42(6), 723-732. https://doi.org/10.12989/scs.2022.42.6.723.
  23. Madenci, E. (2021), "Free vibration and static analyses of metal-ceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. https://doi.org/10.12989/SCS.2021.39.5.493.
  24. Madenci, E. and Ozkilic, Y.O. (2021), "Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157.
  25. Malikan, M., Tornabene, F. and Dimitri, R. (2018), "Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nano-plates using volume integrals", Mater. Res. Express, 5(9), 95006. https://doi.org/10.1088/2053-1591/aad4c3.
  26. Mirjavadi, S.S., Afshari, B.M., Khezel, M., Shafiei, N., Rabby, S. and Kordnejad, M. (2018), "Nonlinear vibration and buckling of functionally graded porous nanoscaled beams", J. Braz. Soc. Mech. Sci. Eng., 40(7), 352. https://doi.org/10.1007/s40430-018-1272-1278.
  27. Norouzzadeh, A., Ansari, R. and Rouhi, H. (2020), "An analytical study on wave propagation in functionally graded nanobeams/tubes based on the integral formulation of nonlocal elasticity", Waves in Random and Complex Media, 30(3), 562-80. https://doi.org/10.1080/17455030.2018.1543979.
  28. Oner, E., Sabano, B.S., Yaylaci, E.U., Adiyaman, G., Yaylaci, M. and Birinci, A. (2022), "On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods", ZAMM-J. Appl. Mathematics and Mechanics,/Zeitschrift Fur Angewandte Mathematik Und Mechanik, 102(2), e202100287. https://doi.org/10.1002/zamm.202100287.
  29. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from fem", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607.
  30. Oner, E., Yaylaci, M. and Birinci, A. (2014), "Solution of a receding contact problem using an analytical method and a finite element method", J. Mech. Mater. Struct., 9(3), 333-345. https://doi.org/ 10.2140/jomms.2014.9.333.
  31. Priyanka, R., Twinkle, C.M. and Pitchaimani, J. (2021), "Stability and dynamic behavior of porous FGM beam: influence of graded porosity, graphene platelets, and axially varying loads", Eng. Comput., 38(5), 4347-4366 https://doi.org/10.1007/s00366-021-01478-5.
  32. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)10970207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  33. Sepehri, S., Mashhadi, M.M. and Fakhrabadi, M.M.S. (2022), "Active/passive tuning of wave propagation in phononic microbeams via piezoelectric patches", Mech. Mater., 167, 104249. https://doi.org/10.1016/j.mechmat.2022.104249.
  34. Shafiei, N. and Kazemi, M. (2017a), "Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.
  35. Shafiei, N. and Kazemi, M. (2017b), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045.
  36. Shafiei, N., Mousavi, A. and Ghadiri, M. (2016), "On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007.
  37. Shahgholian, D., Safarpour, M., Rahimi, A.R. and Alibeigloo, A. (2020), "Buckling analyses of functionally graded graphene-reinforced porous cylindrical shell using the rayleigh-ritz method", Acta Mechanica, 231(5), 1887-1902. https://doi.org/10.1007/s00707-020-02616-8.
  38. Shahsavari, H., Talebitooti, R. and Kornokar, M. (2021), "Analysis of wave propagation through functionally graded porous cylindrical structures considering the transfer matrix method", Thin-Wall. Struct., 159, 107212. https://doi.org/10.1016/j.tws.2020.107212.
  39. Shan, W., Deng, Z., Zhong, H., Mo, H., Han, Z., Yang, Z., Xiang, C., Li, S. and Liu, P. (2020), "Propagation characteristics of longitudinal wave, shear wave and bending wave in porous circular nanoplates", Struct. Eng. Mech., 76(4), 551-559. https://doi.org/10.12989/sem.2020.76.4.551.
  40. Sharifan, M.S. and Jabbari, M. (2020), "Mechanical buckling analysis of saturated porous functionally graded elliptical plates subjected to in-plane force resting on two parameters elastic foundation based on HSDT", J. Pressure Vessel Technol., 142(4), 41302. https://doi.org/10.1115/1.4046707.
  41. Sharma, P. and Khinchi, A. (2021), "On frequency investigation of bi-directional fgm beam under thermal effect", Mater. Today: Proceedings, 47, 6089-6092. https://doi.org/10.1016/j.matpr.2021.05.022.
  42. She, G.L. (2020), "wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct., 37(1), 27-35. https://doi.org/10.12989/scs.2020.37.1.027.
  43. 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/scs.2020.37.1.027
  44. She, G.L., Ren, Y.R. and Yuan, F.G. (2019), "Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems", Steel Compos. Struct., 31, 38-52. https://doi.org/10.12989/scs.2019.31.6.641.
  45. 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, 1-9. https://doi.org/10.1140/epjp/i2018-12196-5.
  46. Srikarun, B., Songsuwan, W. and Wattanasakulpong, N. (2021), "Linear and nonlinear static bending of sandwich beams with functionally graded porous core under different distributed loads", Compos. Struct., 276, 114538. https://doi.org/10.1016/j.compstruct.2021.114538.
  47. Ton-That, H.L., Nguyen-Van, H. and Chau-Dinh, T. (2021), "A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets", Arch. Appl. Mech., 91, 2435-2466. https://doi.org/10.1007/s00419-021-01893-6.
  48. Tran, T.M. and Cuong-Le, T. (2022), "A nonlocal IGA numerical solution for free vibration and buckling analysis of porous sigmoid functionally graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dynam., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  49. Yao, L.Q., Ji, C.J., Shen, J.P. and Li, C. (2020), "Free vibration and wave propagation of axially moving functionally graded timoshenko microbeams", J. Braz. Soc. Mech. Sci. Eng., 42(3), 1-14. https://doi.org/10.1007/s40430-020-2206-9.
  50. Yaylaci, M. (2022), "Simulate of edge and an internal crack problem and estimation of stress intensity factor through finite element method", Adv. Nano Res., 12(4), 405-414. https://doi.org/10.12989/anr.2022.12.4.405.
  51. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  52. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and fem", Comput. Concrete, 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199.
  53. Yaylaci, M., Sabano, B.S., Ozdemir, M.E. and Birinci, A. (2022), "Solving the contact problem of functionally graded layers resting on a hp and pressed with a uniformly distributed load by analytical and numerical methods", Struct. Eng. Mech., 82(3), 401-416. https://doi.org/10.12989/sem.2022.82.3.401.
  54. Yaylaci, E.U., Yaylaci, M., Olmez, H. and Birinci, A. (2020), "Artificial neural network calculations for a receding contact problem", Comput. Concrete 25(6), 551-63. https://doi.org/10.12989/CAC.2020.25.6.551
  55. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143.
  56. Yaylaci, M., Abanoz, M., Yaylaci, E.U., Olmez, H., Sekban, D.M. and Birinci, A. (2022), "Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods", Arch. Appl. Mech., 92(6), 1953-1971. https://doi.org/10.1007/s00419-022-02159-5.
  57. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241.
  58. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Yaylaci, E.U., Oner, E. and Birinci, A. (2021), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/j.mechmat.2020.103730.
  59. Yaylaci, M., Yayli, M., Yaylaci, E.U., Olmez, H. and Birinci, A. (2021), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.
  60. 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.
  61. Zhang, J. and Zheng, W. (2021), "Elastoplastic buckling of fgm beams in thermal environment", Continuum Mech. Thermodynam., 33(1), 151-161. https://doi.org/10.1007/s00161-020-00895-z.
  62. 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.
  63. Zhou, L., Moradi, Z., Al-Tamimi, H.M. and Elhosiny Ali, H. (2022), "On propagation of elastic waves in an embedded sigmoid functionally graded curved beam", Steel Compos. Struct., 44(1), 17-31. https://doi.org/10.12989/scs.2022.44.1.017.