Acknowledgement
The authors acknowledge this work is supported by the first-rate talent introduction project of Chongqing University (02090011044159).
References
- Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: A micromechanical approach", Iran. J. Sci. Technol., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y
- Abdelrahman, A.A., Esen, I., Ozarpa, C. and Eltaher, M. A. (2021), "Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory", Appl. Math. Modell., 96, 215-235. https://doi.org/10.1016/j.apm.2021.03.008
- Abo-Bakr, R.M., Eltaher, M.A. and Attia, M.A. (2022), "Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects", Eng. Comput., 38(1), 255-276. https://doi.org/10.1007/s00366-020-01146-0
- Ahmed, H., Mohamed, Z., Khaled, B. and Tayeb, B. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
- Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
- Akgoz, B. and Civalek, O. (2015), "A novel microstructure-dependent shear deformable beam model", Int. J. Mech. Sci., 99, 10-20. https://doi.org/10.1016/j.ijmecsci.2015.05.003
- 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
- Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. https://doi.org/10.12989/gae.2021.24.1.091
- Bahaadini, R., Hosseini, M. and Khalili-Parizi, Z. (2019), "Electromechanical stability analysis of smart double-nanobeam systems", Euro. Phys. J. Plus, 134(7), 320. https://doi.org/10.1140/epjp/i2019-12644-8
- Barati, M. and Shahverdi, H. (2017), "Hygro-thermal vibration analysis of graded double-refined-nanoplate systems using hybrid nonlocal stress-strain gradient theory", Compos. Struct., 176, 982-995. https://doi.org/10.1016/j.compstruct.2017.06.004
- Barati, M. 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., 168, 885-892. https://doi.org/10.1016/j.compstruct.2017.02.090
- Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical buckling load of triple-walled carbon nanotube based on nonlocal elasticity theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/jnanor.62.108
- Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
- Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircr. Spacecr. Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001
- Bouhadra, A., Menasria, A. and Rachedi, M.A. (2021), "Boundary conditions effect for buckling analysis of porous functionally graded nanobeam", Adv. Nano. Res., 10(4), 313-325. https://doi.org/10.12989/anr.2021.10.4.313
- Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus, 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0
- Civalek, O., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method Appl. Sci., Special Issue Paper. https://doi.org/10.1002/mma.7069
- Civalek, O., Uzun, B. and Yayli, M.O. (2020), "Frequency, bending and buckling loads of nanobeams with different cross sections", Adv. Nano. Res., 9(2), 91-104. https://doi.org/10.12989/anr.2020.9.2.091
- Dai, H. and Safarpour, H. (2021), "Frequency and thermal buckling information of laminated composite doubly curved open nanoshell", Adv. Nano. Res., 10(1), 1-14. https://doi.org/10.12989/anr.2021.10.1.001
- Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano. Res., 10(2), 175-189. https://doi.org/110.12989/anr.2021.10.2.175
- Daikh, A.A., Houari, M.S.A. and Eltaher, M.A. (2021a), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347
- Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021b), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", applied sciences, 11(7), 3250. https://doi.org/10.3390/app11073250
- Dastjerdi, S., Akgoz, B. and Civalek, O. (2020), "On the effect of viscoelasticity on behavior of gyroscopes", Int. J. Eng. Sci., 149, 103236. https://doi.org/10.1016/j.ijengsci.2020.103236
- Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016
- Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://doi.org/10.12989/sem.2021.80.1.063
- Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
- Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concr., 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433
- Ebrahimi, F., Barati, M.R. and Civalek, O. (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366-019-00742-z
- Ebrahimi, F. and Dabbagh, A. (2018a), "NSGT-based acoustical wave dispersion characteristics of thermo-magnetically actuated double-nanobeam systems", Struct. Eng. Sci., 68(6), 701-711. https://doi.org/10.12989/sem.2018.68.6.701
- Ebrahimi, F. and Dabbagh, A. (2018b), "Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems", Struct. Eng. Sci., 67(2), 175-183. https://doi.org/10.12989/sem.2018.67.2.175
- Ebrahimi, F., Dabbagh, A. (2021), "Magnetic field effects on thermally affected propagation of acoustical waves in rotary double-nanobeam systems", Wave Random Complex, 31(1), 25-45. https://doi.org/10.1080/17455030.2018.1558308
- Eyvazian, A., Zhang, C., Musharavati, F., Khan, A. and Mohamed, A.M. (2021), "Elastic wave phenomenon of nanobeams including thickness stretching effect", Adv. Nano. Res., 10(3), 271-280. https://doi.org/10.12989/anr.2021.10.3.271
- 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
- Esmaeilzadeh, M., Golmakani, M.E., Kadkhodayan, M., Amoozgar, M. and Bodaghi, M. (2021), "Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates", Adv. Nano. Res., 10(2), 151-163. https://doi.org/110.12989/anr.2021.10.2.151
- Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38 (4), 3463-3482. https://doi.org/10.1007/s00366-021-01389-5
- Esen, I., Daikh, A.A. and Eltaher, M.A. (2022b), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136(4),1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7
- Fenjan, R.M., Moustafa, N.M., Faleh, N.M. (2020), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano. Res., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283
- Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano. Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
- Ghafarian, M., Shirinzadeh, B. and Wei, W.C. (2020), "Vibration analysis of a rotating cantilever double-tapered AFGM nanobeam", Microsyst. Technol., 26(12), 3657-3676. https://doi.org/10.1007/s00542-020-04837-2
- Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115
- Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano. Res., 10(3), 281-293. https://doi.org/10.12989/anr.2021.10.3.281
- 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
- Khosravi, F., Simyari, M., Hosseini, S.A. and Tounsi, A. (2020), "Size dependent axial free and forced vibration of carbon nanotube via different rod models", Adv. Nano. Res., 9(3), 157-172. https://doi.org/10.12989/anr.2020.9.3.157
- Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013
- Jazi, S.H. (2020), "Nonlinear vibration of an elastically connected double Timoshenko nanobeam system carrying a moving particle based on modified couple stress theory", Arch. Appl. Mech., 90(12), 2739-2754. https://doi.org/10.1007/s00419-020-01746-8
- 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.
- Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428
- Malikan, M. and Eremeyev, V.A. (2020), "A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition", Compos. Struct., 249, 112486. https://doi.org/10.1016/j.compstruct.2020.112486.
- Malikan, M. and Eremeyev, V.A. (2022), "The effect of shear deformations' rotary inertia on the vibrating response of multi-physic composite beam-like actuators", Compos. Struct., 297, 115951. https://doi.org/10.1016/j.compstruct.2022.115951
- Malikan, M., Tornabene, F. and Dimitri, R. (2019), "Transient response of oscillated carbon nanotubes with an internal and external damping", Compos. Part B Eng., 158, 198-205. https://doi.org/10.1016/j.compositesb.2018.09.092
- Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2022), "Thermal buckling of functionally graded piezomagnetic micro-and nanobeams presenting the flexomagnetic effect", Continuum Mech. Thermodyn., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8
- Matouk, H., Bousahla, A.A., Heireche, H., Bourada, F., Bedia, E. A. A., Tounsi, A., Mahmoud, S. R., Tounsi, A. and Benrahou, K. H. (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
- Mousavi, S., Amir, S., Jafari, A. and Arshid, E. (2021), "Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories", Adv. Nano. Res., 10(3), 235-251. https://doi.org/10.12989/anr.2021.10.3.235
- Rahmani, O., Hosseini, S.A.H. and Parhizkari, M. (2017), "Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: A analytical approach", Microsyst. Technol., 23(7), 2739-2751. https://doi.org/10.1007/s00542-016-3127-5
- Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165
- Safari, M., Mohammadimehr, M. and Ashrafi, H. (2021), "Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC", Adv. Nano. Res., 10(2),115-128. https://doi.org/10.12989/anr2021.10.2.115
- Salami, S.J., Boroujerdy, M.S. and Bazzaz, E. (2021), "Geometrically nonlinear thermo-mechanical bending analysis of deep cylindrical composite panels reinforced by functionally graded CNTs", Adv. Nano. Res., 10(4), 385-395. https://doi.org/10.12989/anr.2021.10.4.385
- Shariati, A., Ebrahimi, F., Karimiasl, M., Selvamani, R. and Toghroli, A. (2020), "On bending characteristics of smart magneto-electro-piezoelectric nanobeams system", Adv. Nano. Res., 9(3), 183-191. https://doi.org/10.12989/anr.2020.9.3.183
- She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323
- She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x
- 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/sem.2022.82.2.225
- She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615
- She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407
- 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(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
- Singh, P.P. Azam, M.S. (2021), "Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method", Adv. Nano. Res., 10(1), 25-42. https://doi.org/10.12989/anr.2021.10.1.025
- Tayeb, B., Mohamed, Z., Tahar, H.D. and Khaled, B. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
- Timesli, A. (2020), "Buckling analysis of double walled carbon nanotubes embedded in Kerr elastic medium under axial compression using the nonlocal Donnell shell theory", Adv. Nano. Res., 9(2), 69-82. https://doi.org/110.12989/anr.2020.9.2.069
- Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
- Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
- 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
- Zhang, Y.W., She, G.L. and Ding, H.X. (2023), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A Solids, 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887
- Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293
- Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797
- Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://10.12989/anr.2022.13.5.465
- Zhou, Z., Li, Y. and Fan, J. (2018), "Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method", Physica E, 99, 220-235. https://doi.org/10.1016/j.physe.2018.02.003