Structural Engineering and Mechanics

  • 제80권2호
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  • Pages.231-242
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  • 2021
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Mathematical and computer simulation for Electro-Magneto-Thermo-Elastic Buckling of the Porous Nano system

  • Wang, Xiaohua (Teaching Affairs Office, Zhejiang Guangsha Vocational and Technical University of Construction) ;
  • Wang, Pinyi (Department of Electrical and Computer Engineering, University of Washington Seattle) ;
  • Jiang, Wei (School of Intelligent Manufacturing, Zhejiang Guangsha Vocational and Technical University of Construction) ;
  • Wu, Fengqin (Basic Department, Zhejiang Guangsha Vocational and Technical University of Construction) ;
  • Kiani, Masoud (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arefi, Mohammad (Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2020.06.15
  • 심사 : 2021.09.10
  • 발행 : 2021.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

Buckling analysis of porous sandwich nanoplate integrated with two piezoelectric face-sheets is presented based on shear and normal deformation theory (SNTD). Effect of small scales of the porous core and actuated face-sheets is accounted based on the nonlocal strain gradient theory (NSGT). Large parametric results are presented to investigate variation of various critical loads in terms of significant parameters such as porosity volume fraction, strain gradient and nonlocal parameter, and dimensionless geometric parameters. It is concluded that increase of porosity volume fraction leads to decrease of critical electric and magnetic potentials and increase of critical temperatures.

키워드

참고문헌

  1. Ahmadi, H. and Foroutan, K. (2019), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel. Compos. Struct., 32(2), 253-264. https://doi.org/10.12989/scs.2019.32.2.253.
  2. Arefi, M. (2014), "A complete set of equations for piezomagnetoelastic analysis of a functionally graded thick shell of revolution", Lat. Am. J. Solid. Struct., 11, 2073-2092. https://doi.org/10.1590/S1679-78252014001100009
  3. Arefi, M. and Rahimi, G.H. (2012), "Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure", Smart. Struct. Syst., 9(2), 127-143. http://doi.org/10.12989/sss.2012.9.2.127.
  4. Arefi, M. and Zenkour, A.M. (2017), "Transient analysis of a three-layer microbeam subjected to electric potential", Int. J. Smart. Nano. Mater., 8(1), 20-40. https://doi.org/10.1080/19475411.2017.1292967.
  5. Arefi, M. and Zenkour, A.M. (2018), "Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory", J. Intel. Mater. Syst. Struct., 29(7), 1394-1406. https://doi.org/10.1177/1045389X17733333.
  6. Arefi, M., Karroubi, R. and Irani-Rahaghi, M. (2016), "Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer", Appl. Math. Mech., 37(7), 821-834. https://doi.org/10.1007/s10483-016-2098-9.
  7. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. B. Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057.
  8. Arefi, M., Kiani, M. and Zenkour, A.M. (2020), "Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak's foundation via MCST", J. Sandw. Struct. Mater., 22(1), 55-86. https://doi.org/10.1177/1099636217734279.
  9. Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2013), "Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field", Smart. Struct. Syst., 9(5), 427-439. https://doi.org/10.12989/sss.2012.9.5.427.
  10. Chen, G., Zhang, F., Zhou, Z., Li, J. and Tang, Y. (2018), "A flexible dual-ion battery based on PVDF-HFP-modified gel polymer electrolyte with excellent cycling performance and superior rate capability", Adv. Energy Mater., 8(25), 1801219. https://doi.org/10.1002/aenm.201801219.
  11. Cheng, H., Li, T., Li, X., Feng, J., Tang, T. and Qin, D. (2021b), "Facile synthesis of Co9S8 nanocages as an electrochemical sensor for luteolin detection", J. Electrochem. Soc., 168(8), 087504. https://doi.org/10.1149/1945-7111/ac1813.
  12. Cheng, J., Tan, Z., Xing, Y., Shen, Z., Zhang, Y., Liu, L. and Liu, S. (2021a), "Exfoliated conjugated porous polymer nanosheets for highly efficient photocatalytic hydrogen evolution", J. Mater. Chem. A, 9(9), 5787-5795. https://doi.org/10.1039/D0TA11479K.
  13. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2020), "Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect", Defence Technol., 17(1), 119-134. https://doi.org/10.1016/j.dt.2020.01.001.
  14. Du, Y., Pan, N., Xu, Z., Deng, F., Shen, Y. and Kang, H. (2020), "Pavement distress detection and classification based on YOLO network", Int. J. Pavement. Eng., 1-14. https://doi.org/10.1080/10298436.2020.1714047.
  15. Eringen, A. and Wegner, J. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56, B20-B22. https://doi.org/10.1115/1.1553434.
  16. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  17. Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M. and Mohammadi, M. (2016), "Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates", Compos. Struct., 140, 323-336. https://doi.org/10.1016/j.compstruct.2015.12.039.
  18. Guo, J., Xiao, C., Gao, J., Li, G., Wu, H., Chen, L. and Qian, L. (2021a), "Interplay between counter-surface chemistry and mechanical activation in mechanochemical removal of N-faced GaN surface in humid ambient", Trib. Int., 159, 107004. https://doi.org/10.1016/j.triboint.2021.107004.
  19. Guo, X., Zhang, C., Tian, Q. and Yu, D. (2021b), "Liquid metals dealloying as a general approach for the selective extraction of metals and the fabrication of nanoporous metals: A review", Mater. Today. Commun., 26, 102007. https://doi.org/10.1016/j.mtcomm.2020.102007.
  20. Hosseini-Hashemi, Sh. and Bakhshi Khaniki, H. (2018), "Three dimensional dynamic response of functionally graded nanoplates under a moving load", Struct. Eng. Mech., 66(2), 249-262. https://doi.org/10.12989/sem.2018.66.2.249.
  21. Hu, L., Huang, X., Zhang, S., Chen, X., Dong, X., Jin, H. and Jiang, Z. (2021), "MoO.sub.3 structures transition from nanoflowers to nanorods and their sensing performances", J. Mater. Sci. Mater. Electron., 32(19), 23728. https://doi.org/10.1007/s10854-021-06464-7.
  22. Jena, S.K., Chakraverty, S. and Malikan, M. (2020), "Vibration and buckling characteristics of nonlocal beam placed in a magnetic field embedded in Winkler-Pasternak elastic foundation using a new refined beam theory: an analytical approach", Eur. Phys. J. Plus., 135(2), 164. https://doi.org/10.1140/epjp/s13360-020-00176-3.
  23. Kakar, R. and Kakar, S. (2016), "Shear wave in a fiber-reinforced anisotropic layer overlying a pre-stressed porous half space with self-weight", Smart. Struct. Syst., 18(5), 911-930. https://doi.org/10.12989/sss.2016.18.5.911.
  24. Khoshgoftar, M., Rahimi, M.J. and Arefi, G.H. (2013), "Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure", Mech. Res. Commun., 51, 61-66. https://doi.org/10.1016/j.mechrescom.2013.05.001.
  25. Kiani, K., Asil Gharebaghi, S. and Mehri, B. (2017), "In-plane and out-of-plane waves in nanoplates immersed in bidirectional magnetic fields", Struct. Eng. Mech., 61(1), 65-76. https://doi.org/10.12989/sem.2017.61.1.065.
  26. Kovalnogov, V.N., Simos, T.E. and Tsitouras, C. (2021), "Runge-Kutta pairs suited for SIR-type epidemic models", Math. Meth. Appl. Sci., 44(6), 5210-5216. https://doi.org/10.1002/mma.7104.
  27. Lei, Z., Hao, S., Yang, J., Zhang, L., Fang, B., Wei, K. and Weif, C. (2020), "Study on denitration and sulfur removal performance of Mn-Ce supported fly ash catalyst", Chemosphere (Oxford), 128646. https://doi.org/10.1016/j.chemosphere.2020.128646.
  28. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013.
  29. Li, L., Hu, Y. and Li, X. (2016), "Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory", Int. J. Mech. Sci., 115-116, 135-144. https://doi.org/10.1016/j.ijmecsci.2016.06.011.
  30. Li, Q., Wu, D., Chen, X., Liu, L., Yu, Y. and Gao, W. (2018), "Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation", Int. J. Mech. Sci., 148, 596-610. https://doi.org/10.1016/j.ijmecsci.2018.09.020.
  31. Li, X., Dong, Z., Yu, P., Wang, L., Niu, X., Yamaguchi, H. and Li, D. (2021a), "Effect of self-assembly on fluorescence in magnetic multiphase flows and its application on the novel detection for COVID-19", Phys. Fluid., 33(4), 042004. https://doi.org/10.1063/5.0048123.
  32. Li, X., Yang, H., Zhang, J., Qian, G., Yu, H. and Cai, J. (2021b), "Time-domain analysis of tamper displacement during dynamic compaction based on automatic control", Coating., 11(9). https://doi.org/10.3390/coatings11091092.
  33. Li, Y.S., Feng, W.J. and Cai, Z.Y. (2014), "Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory", Compos. Struct., 115, 41-50. https://doi.org/10.1016/j.compstruct.2014.04.005.
  34. 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. Solid., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001.
  35. Liu, C., Gao, X., Chi, D., He, Y., Liang, M. and Wang, H. (2021), "On-line chatter detection in milling using fast kurtogram and frequency band power", Eur. J. Mech. A, Solid., 90, 104341. https://doi.org/10.1016/j.euromechsol.2021.104341
  36. Lu, Z., Zhao, L., Ding, H. and Chen, L. (2021), "A dual-functional metamaterial for integrated vibration isolation and energy harvesting", J. Sound. Vib., 509, 116251. https://doi.org/10.1016/j.jsv.2021.116251.
  37. Mashat, D.S., Zenkour, A.M. and Radwan, A.F. (2020), "A quasi 3-D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity", Eur. J. Mech-A/Solid., 82, 103985. https://doi.org/10.1016/j.euromechsol.2020.103985.
  38. Medvedev, M.A., Simos, T.E. and Tsitouras, Ch. (2020), "Explicit, eighth-order, four-step methods for solving y"=f(x,y)", Bull. Malays. Math. Sci. Soc., 43(5), 3791-3807. https://doi.org/10.1007/s40840-019-00879-6.
  39. Medvedeva, M.A., Katsikis, V.N., Mourtas, S.D. and Simos, T.E. (2021a), "Randomized time-varying knapsack problems via binary beetle antennae search algorithm: Emphasis on applications in portfolio insurance", Math. Meth. Appl. Sci., 44(2), 2002-2012. https://doi.org/10.1002/mma.6904.
  40. Medvedeva, M.A., Simos, T.E. and Tsitouras, C. (2021b), "Exponential integrators for linear inhomogeneous problems", Math. Meth. Appl. Sci., 44(1), 937-944. https://doi.org/10.1002/mma.6802.
  41. Mou, B. and Bai, Y. (2018), "Experimental investigation on shear behavior of steel beam-to-CFST column connections with irregular panel zone", Eng. Struct., 168, 487-504. https://doi.org/10.1016/j.engstruct.2018.04.029.
  42. Nguyen, L.B., Thai, C.H., Zenkour, A.M. and Nguyen-Xuan, H. (2019), "An isogeometric Bezier finite element method for vibration analysis of functionally graded piezoelectric material porous plates", Int. J. Mech. Sci., 157-158, 165-183. https://doi.org/10.1016/j.ijmecsci.2019.04.017.
  43. Ni, Z., Cao, X., Wang, X., Zhou, S., Zhang, C., Xu, B., and Ni, Y. (2021), "Facile synthesis of Copper(I) oxide nanochains and the photo-thermal conversion performance of its nanofluids", Coating., 11, 749. https://doi.org/10.3390/coatings11070749.
  44. Phung-Van, P., Ferreira, A.J.M. and Thai, C.H. (2020), "Computational optimization for porosity-dependent isogeometric analysis of functionally graded sandwich nanoplates", Compos. Struct., 239, 112029. https://doi.org/10.1016/j.compstruct.2020.112029.
  45. Phung-Van, P., Ferreira, A.J.M. and Thai, C.H. (2020), "Computational optimization for porosity-dependent isogeometric analysis of functionally graded sandwich nanoplates", Compos. Struct., 239, 112029. https://doi.org/10.1016/j.compstruct.2020.112029.
  46. Rahmani, M., Mohammadi, Y. and Kakavand, F. (2020), "Buckling analysis of different types of porous FG conical sandwich shells in various thermal surroundings", J. Brazil. Soc. Mech. Sci. Eng., 42(4), 1-16. https://doi.org/10.1007/s40430-020-2200-2.
  47. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs", Compos. Struct., 198, 51-62. https://doi.org/10.1016/j.compstruct.2018.05.031.
  48. Shahgholian, D., Safarpour, M., Rahimi, A.R. and Alibeigloo, A. (2020), "Buckling analyses of functionally graded graphenereinforced porous cylindrical shell using the Rayleigh-Ritz method", Acta Mech.,1-16. https://doi.org/10.1007/s00707-020-02616-8.
  49. Shariati, M., Heyrati, A., Zandi, Y., Laka, H., Toghroli, A., Kianmehr, P., ... & Poi-Ngian, S. (2019), "Application of waste tire rubber aggregate in porous concrete", Smart Struct. Syst., 24(4), 553-566. https://doi.org/10.12989/sss.2019.24.4.553.
  50. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.
  51. Simos, T.E. and Tsitouras, C. (2020), "Explicit, ninth order, two step methods for solving inhomogeneous linear problems x"(t)=Lambda x(t) plus f(t)", Appl. Numer. Math., 153, 344-351. https://doi.org/10.1016/j.apnum.2020.03.003.
  52. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., 63(3), 401-415. https://doi.org/10.12989/sem.2017.63.3.401.
  53. Sobhy, M. and Zenkour, A.M. (2018), "Nonlocal thermal and mechanical buckling of nonlinear orthotropic viscoelastic nanoplates embedded in a Visco-Pasternak medium", Int. J. Appl. Mech., 10(8), 1850086. https://doi.org/10.1142/S1758825118500862.
  54. Sun, J., Aslani, F., Wei, J. and Wang, X. (2021), "Electromagnetic absorption of copper fiber oriented composite using 3D printing", Constr. Build. Mater., 300, 124026. https://doi.org/10.1016/j.conbuildmat.2021.124026.
  55. Thai, C.H., Zenkour, A.M., Abdel Wahab, M. and Nguyen-Xuan, H. (2016), "A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis", Compos. Struct., 139, 77-95. https://doi.org/10.1016/j.compstruct.2015.11.066
  56. Toghroli, A., Shariati, M., Sajedi, F., Ibrahim, Z., Koting, S., Mohamad, E.T. and Khorami, M. (2018), "A review on pavement porous concrete using recycled waste materials", Smart. Struct. Syst., 22(4), 433-440 . https://doi.org/10.12989/sss.2018.22.4.433.
  57. Wang, C.Y., Murmu, T. and Adhikari, S. (2011), "Mechanisms of nonlocal effect on the vibration of nanoplates", Appl. Phys. Let., 98(15), 153101. https://doi.org/10.1063/1.3579249.
  58. Wang, Y., Li, C., Zhang, Y., Yang, M., Li, B., Jia, D. and Mao, C. (2016), "Experimental evaluation of the lubrication properties of the wheel/workpiece interface in minimum quantity lubrication (MQL) grinding using different types of vegetable oils", J. Clean. Prod., 127, 487-499. https://doi.org/10.1016/j.jclepro.2016.03.121.
  59. Wang, Y.Q. (2018), "Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state", Acta Astronautica, 143, 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004.
  60. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  61. Wu, X., Li, C., Zhou, Z., Nie, X., Chen, Y., Zhang, Y. and Sharma, S. (2021), "Circulating purification of cutting fluid: an overview", Int. J. Adv. Manuf. Tech., 1-36. https://doi.org/10.1007/s00170-021-07854-1.
  62. Xie, Y., Meng, X., Mao, D., Qin, Z., Wan, L. and Huang, Y. (2021), "Homogeneously dispersed graphene nanoplatelets as long-term corrosion inhibitors for aluminum matrix composites", ACS Appl. Mater. Interf., 13(27), 32161-32174. https://doi.org/10.1021/acsami.1c07148.
  63. Xu, X. and Nieto-Vesperinas, M. (2019), "Azimuthal imaginary poynting momentum density", Phys. Rev. Let., 123(23), 233902. https://doi.org/10.1103/PhysRevLett.123.233902.
  64. Xu, X., Karami, B. and Shahsavari, D. (2021), "Time-dependent behavior of porous curved nanobeam", Int. J. Eng. Sci., 160, 103455. https://doi.org/10.1016/j.ijengsci.2021.103455.
  65. Xu, X.J., Wang, X.C., Zheng, M.L. and Ma, Z. (2017), "Bending and buckling of nonlocal strain gradient elastic beams", Compos. Struct., 160, 366-377. https://doi.org/10.1016/j.compstruct.2016.10.038.
  66. Xue, C., You, J., Zhang, H., Xiong, S., Yin, T. and Huang, Q. (2021), "Capacity of myofibrillar protein to adsorb characteristic fishy-odor compounds: Effects of concentration, temperature, ionic strength, pH and yeast glucan addition", Food Chem., 363, 130304. https://doi.org/10.1016/j.foodchem.2021.130304.
  67. Ye, R., Liu, P., Shi, K. and Yan, B. (2020), "State damping control: a novel simple method of rotor UAV with high performance", IEEE Access, 8, 214346-214357. https://doi.org/10.1109/ACCESS.2020.3040779.
  68. Zenkour, A.M. and Aljadani, M.H. (2019), "Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates", Eur. J. Mech-A/Solid., 78, 103835. https://doi.org/10.1016/j.euromechsol.2019.103835.
  69. Zenkour, A.M. and Radwan, A.F. (2020), "Nonlocal mixed variational formula for orthotropic nanoplates resting on elastic foundations", The. Eur. Phys. J. Plus., 135, 493. https://doi.org/10.1140/epjp/s13360-020-00504-7.
  70. Zhang, M., Zhang, L., Tian, S., Zhang, X., Guo, J., Guan, X. and Xu, P. (2020a), "Effects of graphite particles/Fe3+ on the properties of anoxic activated sludge", Chemosphere (Oxford), 253, 126638. https://doi.org/10.1016/j.chemosphere.2020.126638.
  71. Zhang, S., Zhao, S., Huang, S., Hu, B., Wang, M., Zhang, Z. and Du, M. (2021), "Photocatalytic degradation of oxytetracycline under visible light by nanohybrids of CoFe alloy nanoparticles and nitrogen-/sulfur-codoped mesoporous carbon", Chem. Eng. J., 420, 130516. https://doi.org/10.1016/j.cej.2021.130516.
  72. Zhang, X., Sun, X., Lv, T., Weng, L., Chi, M., Shi, J. and Zhang, S. (2020b), "Preparation of PI porous fiber membrane for recovering oil-paper insulation structure", J. Math. Sci. Mater. Elec., 31(16), 13344-13351. https://doi.org/10.1007/s10854-020-03888-5.
  73. Zhang, X., Tang, Y., Zhang, F. and Lee, C. (2016), "a novel aluminum-graphite dual-ion battery", Adv. Energy. Mater., 6(11), 1502588. https://doi.org/10.1002/aenm.201502588.
  74. Zhang, Y., Li, H.N., Li, C.H., Huang, C.Z., Ali, H.M., Xu, X.F., ... & Said, Z. (2021), "Nano-enhanced biolubricant in sustainable manufacturing: from processability to mechanisms", Friction. https://doi.org/10.1007/s40544-021-0536-y.
  75. Zhao, N., Deng, L., Luo, D. and Zhang, P. (2020b), "One-step fabrication of biomass-derived hierarchically porous carbon/MnO nanosheets composites for symmetric hybrid supercapacitor", Appl. Surf. Sci., 526, 146696. https://doi.org/10.1016/j.apsusc.2020.146696.
  76. Zhao, R., Zhang, L., Guo, B., Chen, Y., Fan, G., Jin, Z. and Zhu, J. (2021), "Unveiling substitution preference of chromium ions in sulphoaluminate cement clinker phases", Compos. Part B. Eng., 222, 109092. https://doi.org/10.1016/j.compositesb.2021.109092
  77. Zhao, X., Chen, B., Li, Y.H., Zhu, W.D., Nkiegaing, F.J. and Shao, Y.B. (2020c), "Forced vibration analysis of Timoshenko double-beam system under compressive axial load by means of Green's functions", J. Sound. Vib., 464, 115001. https://doi.org/10.1016/j.jsv.2019.115001.
  78. Zhao, X., Zhu, W.D. and Li, Y.H. (2020a), "Analytical solutions of nonlocal coupled thermoelastic forced vibrations of micro-/nano-beams by means of Green's functions", J. Sound. Vib., 481, 115407. https://doi.org/10.1016/j.jsv.2020.115407.
  79. Zhong, Q., Yang, J., Shi, K., Zhong, S., Zhixiong, L. and Angel, S.M. (2021), "Event-triggered H∞ load frequency control for multi-area nonlinear power systems based on non-fragile proportional integral control strategy", IEEE Trans. Intel. Tran. Syst., 1-11. https://doi.org/10.1109/TITS.2021.3110759.