Steel and Composite Structures

  • 제44권1호
  • /
  • Pages.17-31
  • /
  • 2022
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  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On propagation of elastic waves in an embedded sigmoid functionally graded curved beam

  • Zhou, Linyun (School of Transportation, Southeast University) ;
  • Moradi, Zohre (Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University) ;
  • Al-Tamimi, Haneen M. (Air Conditioning and Refrigeration Techniques Engineering Department, Al-Mustaqbal University College) ;
  • Ali, H. Elhosiny (Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University)
  • 투고 : 2021.10.31
  • 심사 : 2022.06.21
  • 발행 : 2022.07.10
⟨ 이전 논문 다음 논문 ⟩

초록

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

키워드

과제정보

This work was supported by National Science Foundation of China (51808208). The authors express their appreciation to the Deanship of Scientific Research at King Khalid University, Saudi Arabia, for funding this work through research groups program under grant of number R.G.P.2/96/43.

참고문헌

  1. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  2. Alijani, F., Bakhtiari-Nejad, F. and Amabili, M. (2011), "Nonlinear vibrations of FGM rectangular plates in thermal environments", Nonlinear Dynam., 66(3), 251. https://doi.org/10.1007/s11071-011-0049-8
  3. Amiri, A., Rahmani, H. and Ahmadi Balootaki, M. (2020), "Torsional wave propagation in 1D and two dimensional functionally graded rod", J. Comput. Appl. Mech., 51(1), 1-21. https://dx.doi.org/10.22059/jcamech.2019.272234.350.
  4. Chen, Y., Jin, G., Zhang, C., Ye, T. and Xue, Y. (2018), "Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory", Compos. Part B Eng., 153 376-386. https://doi.org/10.1016/j.compositesb.2018.08.111.
  5. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng.,21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  6. Daneshjou, K., Bakhtiari, M. and Tarkashvand, A. (2017), "Wave propagation and transient response of a fluid-filled FGM cylinder with rigid core using the inverse Laplace transform", European J. Mech. A/Solids, 61 420-432. https://doi.org/10.1016/j.euromechsol.2016.10.007.
  7. Dong, Y., Gao, Y., Zhu, Q., Moradi, Z. and Safa, M. (2022), "TEGDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring", Eng. Analysis Boundary Element, 138 95-107. https://doi.org/10.1016/j.enganabound.2022.01.017.
  8. Ebrahimi, F. and Barati, M.R. (2017), "Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory", Proc. Institution Mech. Engineers Part C J. Mech. Eng. Sci., 231(23), 4457-4469. https://doi.org/10.1177/0954406216668912.
  9. Ebrahimi, F. and Dashti, S. (2015), "Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., 19(5), 1279-1298. https://doi.org/10.12989/scs.2015.19.5.1279.
  10. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y.
  11. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019a), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. Comput., 35(4), 1375-1389. https://doi.org/10.1007/s00366-018-0669-4.
  12. Ebrahimi, F. and Seyfi, A. (2020a), "Propagation of flexural waves in anisotropic fluid-conveying cylindrical shells", Symmetry, 12(6), 901. https://doi.org/10.3390/sym12060901.
  13. Ebrahimi, F. and Seyfi, A. (2020b), "Studying propagation of wave in metal foam cylindrical shells with graded porosities resting on variable elastic substrate", Eng. Comput., 38, 379-395. https://doi.org/10.1007/s00366-020-01069-w.
  14. Ebrahimi, F. and Seyfi, A. (2020c), "Wave propagation response of agglomerated multi-scale hybrid nanocomposite plates", Waves Random Complex Media, 32(3), 1-25. https://doi.org/10.1080/17455030.2020.1821933.
  15. Ebrahimi, F. and Seyfi, A. (2021), "Wave propagation response of multi-scale hybrid nanocomposite shell by considering aggregation effect of CNTs", Mech. Based Des. Struct. Machines, 49(1), 59-80. https://doi.org/10.1080/15397734.2019.1666722.
  16. Ebrahimi, F., Seyfi, A. and Dabbagh, A. (2019b), "Wave dispersion characteristics of agglomerated multi-scale hybrid nanocomposite beams", J. Strain Analysis Eng. Design, 54(4), 276-289. https://doi.org/10.1177/0309324719862713.
  17. Ebrahimi, F., Seyfi, A., Nouraei, M. and Haghi, P. (2021a), "Influence of magnetic field on the wave propagation response of functionally graded (FG) beam lying on elastic foundation in thermal environment", Waves Random Complex Media, 1-19. https://doi.org/10.1080/17455030.2020.1847359.
  18. Ebrahimi, F., Seyfi, A. and Teimouri, A. (2021b), "Torsional vibration analysis of scale-dependent non-circular graphene oxide powder-strengthened nanocomposite nanorods", Eng. Comput.,1-12. https://doi.org/10.1007/s00366-021-01528-y.
  19. Esmailpoor Hajilak, Z., Pourghader, J., Hashemabadi, D., Sharifi Bagh, F., Habibi, M. and Safarpour, H. (2019), "Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory", Mech. Based Des. Struct. Machines, 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743.
  20. Fan, L., Huang, Y., Ji, D., Moradi, Z., Safa, M. and Amine Khadimallah, M. (2022), "Interaction of angular velocity and temperature rise in the thermo-inertia bifurcation buckling of FG laminated nanocomposite annular plates", Eng. Struct., 265, 114518. https://doi.org/10.1016/j.engstruct.2022.114518
  21. Fattahi, A. (2019), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., 32(2), 281-292. https://doi.org/10.12989/scs.2019.32.2.281.
  22. Fattahi, A., Safaei, B. and Ahmed, N. (2019), "A comparison for the non-classical plate model based on axial buckling of singlelayered graphene sheets", Europan Phys. J. Plus, 134(11), 555. https://doi.org/10.1140/epjp/i2019-12912-7.
  23. Fu, Y., Chen, H., Guo, R., Huang, Y. and Toroghinejad, M.R. (2021), "Extraordinary strength-ductility in gradient amorphous structured Zr-based alloy", J. Alloys Compounds, 888, 161507. https://doi.org/10.1016/j.jallcom.2021.161507.
  24. Gao, N., Zhang, Z., Deng, J., Guo, X., Cheng, B. and Hou, H. (2022), "Acoustic metamaterials for noise reduction: A review", Adv. Mater. Technol., 7(6), 2100698. https://doi.org/10.1002/admt.202100698.
  25. Ghanati, P. and Safaei, B. (2019), "Elastic buckling analysis of polygonal thin sheets under compression", Indian J. Phys., 93(1), 47-52. https://doi.org/10.1007/s12648-018-1254-9.
  26. Ghassabi, M., Zarastvand, M. and Talebitooti, R. (2019), "Investigation of state vector computational solution on modeling of wave propagation through functionally graded nanocomposite doubly curved thick structures", Eng. Comput., 36, 1417-1433. https://doi.org/10.1007/s00366-019-00773-6.
  27. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2018a), "Forming limit diagrams by including the M-K model in finite element simulation considering the effect of bending", Proc. Institution Mech. Engineers, Part L J. Mater: Des. Appl., 232(8), 625-636. https://doi.org/10.1177/1464420716642258.
  28. Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Performances, 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1.
  29. Habibi, M., Hashemi, R., Tafti, M.F. and Assempour, A. (2018b), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manufact. Processes, 31, 310-323. https://doi.org/10.1016/j.jmapro.2017.11.009.
  30. Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019a), "Wave propagation characteristics of the electrically GNPreinforced nanocomposite cylindrical shell", J. Brazilian Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x.
  31. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019b), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct. Machines, 49(5), 640-658. https://doi.org/10.1080/15397734.2019.1697932.
  32. Habibi, M., Taghdir, A. and Safarpour, H. (2019c), "Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets", Compos. Part B Eng., 175, 107125. https://doi.org/10.1016/j.compositesb.2019.107125.
  33. Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Waves Random Complex Media, 31(6), 1-27. https://doi.org/10.1080/17455030.2019.1662968.
  34. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021), "The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation", Eng. Comput.,1-19. https://doi.org/10.1007/s00366-021-01456-x.
  35. Hu, M., Wang, Y., Yan, Z., Zhao, G., Zhao, Y., Xia, L., Cheng, B., Di, Y. and Zhuang, X. (2021), "Hierarchical dual-nanonet of polymer nanofibers and supramolecular nanofibrils for air filtration with a high filtration efficiency, low air resistance and high moisture permeation", J. Mater. Chemistry A, 9(24), 14093-14100. https://doi.org/10.1039/D1TA01505B.
  36. Huang, X., Zhang, Y., Moradi, Z. and Shafiei, N. (2021a), "Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform microtube", Eng. Comput.,1-18. https://doi.org/10.1007/s00366-021-01395-7.
  37. Huang, X., Zhu, Y., Vafaei, P., Moradi, Z. and Davoudi, M. (2021b), "An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate", Eng. Comput., https://doi.org/10.1007/s00366-021-01320-y.
  38. Huynh, T.A., Luu, A.T. and Lee, J. (2017), "Bending, buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach", Meccanica, 52(11-12), 2527-2546. https://doi.org/10.1007/s11012-016-0603-z.
  39. Jiao, J., Ghoreishi, S.-m., Moradi, Z. and Oslub, K. (2021), "Coupled particle swarm optimization method with genetic algorithm for the static-dynamic performance of the magnetoelectro- elastic nanosystem", Eng. Comput., https://doi.org/10.1007/s00366-021-01391-x.
  40. Kumar, R., Lal, A., Singh, B. and Singh, J. (2019), "New transverse shear deformation theory for bending analysis of FGM plate under patch load", Compos. Struct., 208, 91-100. https://doi.org/10.1016/j.compstruct.2018.10.014.
  41. Kurtaran, H. (2015), "Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method", Compos. Struct., 131, 821-831. https://doi.org/10.1016/j.compstruct.2015.06.024.
  42. Li, C., Han, Q., Liu, Y. and Xiao, D. (2017), "Guided wave propagation in rotating functionally graded annular plates", Acta Mechanica, 228(3), 1083-1095. https://doi.org/10.1007/s00707-016-1752-9.
  43. Lim, C.W., Yang, Q. and Lu, C. (2009), "Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches", Compos. Struct., 90(3), 323-329. https://doi.org/10.1016/j.compstruct.2009.03.014.
  44. Liu, C., Zhao, Y., Wang, Y., Zhang, T. and Jia, H. (2021a), "Hybrid dynamic modeling and analysis of high-speed thin-rimmed gears", J. Mech. Des., 143(12), https://doi.org/10.1115/1.4051137.
  45. Liu, T., Wang, A., Wang, Q. and Qin, B. (2020), "Wave based method for free vibration characteristics of functionally graded cylindrical shells with arbitrary boundary conditions", Thin- Walled Struct., 148, 106580. https://doi.org/10.1016/j.tws.2019.106580.
  46. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021b), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput.,1-23. https://doi.org/10.1007/s00366-021-01454-z.
  47. Luo, J., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Effect of simultaneous compressive and inertia loads on the bifurcation stability of shear deformable functionally graded annular fabrications reinforced with graphenes", European J. Mech. A/Solids, 104581. https://doi.org/10.1016/j.euromechsol.2022.104581.
  48. Ma, L., Liu, X. and Moradi, Z. "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput.,1-25. https://doi.org/10.1007/s00366-020-01210-9.
  49. Malekzadeh, P., Haghighi, M.G. and Atashi, M. (2010), "Out-ofplane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92(2), 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040.
  50. Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E., Tounsi, A., Mahmoud, S., Tounsi, A. and Benrahou, K. (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.
  51. Michael, M., Meyyazhagan, A., Velayudhannair, K., Pappuswamy, M., Maria, A., Xavier, V., Balasubramanian, B., Baskaran, R., Kamyab, H. and Vasseghian, Y. (2022), "The Content of Heavy Metals in Cigarettes and the Impact of Their Leachates on the Aquatic Ecosystem", Sustainability, 14(8), 4752. https://doi.org/10.3390/su14084752.
  52. Mohamed, N., Eltaher, M., Mohamed, S. and Seddek, L. (2018), "Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations", J. Non-Linear Mech., 101, 157-173. https://doi.org/10.1016/j.ijnonlinmec.2018.02.014.
  53. Moradi, Z., Davoudi, M., Ebrahimi, F. and Ehyaei, A.F. (2021), "Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller", Waves Random Complex Media, 1-24. https://doi.org/10.1080/17455030.2021.1926572.
  54. Nebab, M., Atmane, H.A., Bennai, R., Tounsi, A. and Bedia, E. (2019), "Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT", Struct. Eng. Mech., 69(5), 511-525. https://doi.org/10.12989/sem.2019.69.5.511.
  55. Parandvar, H. and Farid, M. (2016), "Large amplitude vibration of FGM plates in thermal environment subjected to simultaneously static pressure and harmonic force using multimodal FEM", Compos. Struct., 141, 163-171. https://doi.org/10.1016/j.compstruct.2016.01.044.
  56. Paul, A. and Das, D. (2016), "Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness", Eng. Sci. Technol., 19(3), 1608-1625. https://doi.org/10.1016/j.jestch.2016.05.014s.
  57. Peng, Y., Xu, Z., Wang, M., Li, Z., Peng, J., Luo, J., Xie, S., Pu, H. and Yang, Z. (2021), "Investigation of frequency-up conversion effect on the performance improvement of stack-based piezoelectric generators", Renewable Energy, 172, 551-563. https://doi.org/10.1016/j.renene.2021.03.064.
  58. Piovan, M.T., Domini, S. and Ramirez, J.M. (2012), "In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beams", Compos. Struct., 94(11), 3194-3206. https://doi.org/10.1016/j.compstruct.2012.04.032.
  59. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041.
  60. Pradhan, S. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321(1-2), 342-362. https://doi.org/10.1016/j.jsv.2008.09.018.
  61. Pydah, A. and Sabale, A. (2017), "Static analysis of bi-directional functionally graded curved beams", Compos. Struct., 160, 867-876. https://doi.org/10.1016/j.compstruct.2016.10.120.
  62. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., 22(2), 119. https://doi.org/10.12989/gae.2020.22.2.119.
  63. Rajasekaran, S. (2014), "Analysis of curved beams using a new differential transformation based curved beam element", Meccanica, 49(4), 863-886. https://doi.org/10.1007/s11012-013-9835-3.
  64. Rastgo, A., Shafie, H. and Allahverdizadeh, A. (2005), "Instability of curved beams made of functionally graded material under thermal loading", J. Mech. Mater. Des., 2(1-2), 117-128. https://doi.org/10.1007/s10999-005-4446-3.
  65. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  66. Safaei, B. (2020), "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct., 35(5), 659-670. https://doi.org/10.12989/scs.2020.35.5.659.
  67. Safaei, B. (2021), "Frequency-dependent damped vibrations of multifunctional foam plates sandwiched and integrated by composite faces", Europan Phys. J. Plus, 136(6), 1-16. https://doi.org/10.1140/epjp/s13360-021-01632-4.
  68. Safaei, B. and Fattahi, A. (2017), "Free vibrational response of single-layered graphene sheets embedded in an elastic matrix using different nonlocal plate models", Mechanics, 23(5), 678-687. https://doi.org/10.5755/j01.mech.23.5.14883.
  69. Safaei, B., Fattahi, A. and Chu, F. (2018), "Finite element study on elastic transition in platelet reinforced composites", Microsyst. Technol., 24(6), 2663-2671. https://doi.org/10.1007/s00542-017-3651-y.
  70. Safaei, B., Naseradinmousavi, P. and Rahmani, A. (2016), "Development of an accurate molecular mechanics model for buckling behavior of multi-walled carbon nanotubes under axial compression", J. Molecular Graphics Modelling, 65, 43-60. https://doi.org/10.1016/j.jmgm.2016.02.001.
  71. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019), "A sizedependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation", J. Mech. Mater. Des., 15(3), 569-583. https://doi.org/10.1007/s10999-018-9431-8.
  72. Sahmani, S. and Safaei, B. (2021), "Microstructural-dependent nonlinear stability analysis of random checkerboard reinforced composite micropanels via moving Kriging meshfree approach", Europan Phys. J. Plus, 136(8), 1-31. https://doi.org/10.1140/epjp/s13360-021-01706-3.
  73. Sayyad, A.S. and Ghugal, Y.M. (2019), "A sinusoidal beam theory for functionally graded sandwich curved beams", Compos. Struct., 226, 111246. https://doi.org/10.1016/j.compstruct.2019.111246.
  74. Seyfi, A. and Aghdam, M. (2021), "Vibrational behavior of temperature-dependent imperfect functionally graded plate lying on an elastic substrate", Mech. Based Des. Struct. Machines, 1-22. https://doi.org/10.1080/15397734.2021.1944189.
  75. Seyfi, A., Teimouri, A., Dimitri, R. and Tornabene, F. (2022), "Dispersion of elastic waves in functionally graded cntsreinforced composite beams", Appl. Sci., 12(8), 3852. https://doi.org/10.3390/app12083852.
  76. 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.
  77. Sobhy, M. (2016), "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment", J. Mech. Sci., 110, 62-77. https://doi.org/10.1016/j.ijmecsci.2016.03.003.
  78. Sofiyev, A. (2012), "The non-linear vibration of FGM truncated conical shells", Compos. Struct., 94(7), 2237-2245. https://doi.org/10.1016/j.compstruct.2012.02.005.
  79. Sun, Y., Li, S.R. and Batra, R.C. (2016), "Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation", J. Thermal Stresses, 39(1), 11-26. https://doi.org/10.1080/01495739.2015.1120627.
  80. Szekrenyes, A. (2007), "Improved analysis of unidirectional composite delamination specimens", Mech. Mater., 39(10), 953-974. https://doi.org/10.1016/j.mechmat.2007.04.002.
  81. Tounsi, A., Al-Dulaijan, S., Al-Osta, M.A., Chikh, A., Al-Zahrani, M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a twoparameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  82. Wang, G., Liu, D., Fan, S., Li, Z. and Su, J. (2021a), "High-k erbium oxide film prepared by sol-gel method for low-voltage thin-film transistor", Nanotechnology, 32(21), 215202. https://doi.org/10.1088/1361-6528/abe439.
  83. Wang, H., Habibi, M., Marzouki, R., Majdi, A., Shariati, M., Denic, N., Zakic, A., Khorami, M., Khadimallah, M.A. and Ebid, A.A.K. (2022a), "Improving the self-healing of cementitious materials with a hydrogel system", Gels, 8(5), 278. https://doi.org/10.3390/gels8050278.
  84. Wang, H., Wu, X., Zheng, X. and Yuan, X. (2021b), "Virtual voltage vector based model predictive control for a nine-phase open-end winding PMSM with a common DC bus", IEEE Transactions Industrial Electronics, 69(6), 5386-5397. https://doi.org/10.1109/TIE.2021.3088372.
  85. Wang, X., Jin, C. and Yuan, Z. (2020), "Free vibration of FGM annular sectorial plates with arbitrary boundary supports and large sector angles", Mech. Based Des. Struct. Machines, 50(1), 331-351. https://doi.org/10.1080/15397734.2020.1717342.
  86. Wang, Y., Yang, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022b), "Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation", European J. Mech. A/Solids, 95, 104638. https://doi.org/10.1016/j.euromechsol.2022.104638.
  87. Xia, W., Du, J., Habibi, M., Shariati, M. and Khadimallah, M.A. (2022), "Application of Chebyshev-based GDQ and Newmark methods to viscothermoelasticity responses of FG composite annular systems", Eng. Analysis Boundary Element, 143, 28-42. https://doi.org/10.1016/j.enganabound.2022.06.003.
  88. Xie, X. and Chen, D. (2022), "Data-driven dynamic harmonic model for modern household appliances", Appl. Energy, 312, 118759. https://doi.org/10.1016/j.apenergy.2022.118759
  89. Xu, C. and Yu, Z. (2017), "Numerical simulation of elastic wave propagation in functionally graded cylinders using time-domain spectral finite element method", Adv. Mech. Eng., 9(11), 1687814017734457. https://doi.org/10.1177/1687814017734457.
  90. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021), "Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution", Compos. Struct., 275, 114395. https://doi.org/10.1016/j.compstruct.2021.114395.
  91. Yan, W., Cao, M., Fan, S., Liu, X., Liu, T., Li, H. and Su, J. (2021a), "Multi-yolk ZnSe/2 (CoSe2)@ NC heterostructures confined in N-doped carbon shell for high-efficient sodium-ion storage", Compos. Part B Eng., 213, 108732. https://doi.org/10.1016/j.compositesb.2021.108732.
  92. Yan, W., Liang, K., Chi, Z., Liu, T., Cao, M., Fan, S., Xu, T., Liu, T. and Su, J. (2021b), "Litchi-like structured MnCo2S4@ C as a high capacity and long-cycling time anode for lithium-ion batteries", Electrochimica Acta, 376, 138035. https://doi.org/10.1016/j.electacta.2021.138035.
  93. Yang, N., Moradi, Z., Khadimallah, M.A. and Arvin, H. (2022), "Application of the Chebyshev-Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment", Eng. Analysis Boundary Element, 139, 169-179. https://doi.org/10.1016/j.enganabound.2022.03.013.
  94. Yang, Z., Lu, H., Sahmani, S. and Safaei, B. (2021), "Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness", Archives Civil Mech. Eng., 21(3), 1-19. https://doi.org/10.1007/s43452-021-00264-w.
  95. Yousefi, A. and Rastgoo, A. (2011), "Free vibration of functionally graded spatial curved beams", Compos. Struct., 93(11), 3048-3056. https://doi.org/10.1016/j.compstruct.2011.04.024.
  96. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic highorder computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Processing, 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373.
  97. Yuan, Y., Zhao, X., Zhao, Y., Sahmani, S. and Safaei, B. (2021), "Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation", Thin-Walled Struct., 159, 107249. https://doi.org/10.1016/j.tws.2020.107249.
  98. Zhang, H., Liu, Y. and Deng, Y. (2021), "Temperature gradient modeling of a steel box-girder suspension bridge using Copulas probabilistic method and field monitoring", Adv. Struct. Eng., 24(5), 947-961. https://doi.org/10.1177/1369433220971779.
  99. Zhao, J., Wang, Q., Deng, X., Choe, K., Xie, F. and Shuai, C. (2019), "A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams", Compos. Part B Eng., 165, 155-166. https://doi.org/10.1016/j.compositesb.2018.11.080.
  100. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. "Bending and stress responses of the hybrid axisymmetric system via statespace method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.
  101. Zhou, J., Bai, J. and Liu, Y. (2022), "Fabrication and modeling of matching system for air-coupled transducer", Micromachines, 13(5), 781. https://doi.org/10.3390/mi13050781.
  102. Zhu, L., Ren, H., Habibi, M., Mohammed, K.J. and Khadimallah, M.A. (2022), "Predicting the environmental economic dispatch problem for reducing waste nonrenewable materials via an innovative constraint multi-objective Chimp Optimization Algorithm", J. Cleaner Production, 132697. https://doi.org/10.1016/j.jclepro.2022.132697.