Exact analysis of local/nonlocal vibration in nanobeams on elastic foundations with arbitrary supports and tip masses
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OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Thermoelastic and Magnetoelastic Phenomena · Composite Structure Analysis and Optimization
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References (100+)
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1. Abdelrahman, A.A., Abdelwahed, M.S., Ahmed, H.M., Hamdi, A., Eltaher, M.A.: Investigation of size-dependent vibration behavior of piezoelectric composite nanobeams embedded in an elastic foundation considering flexoelectricity effects. Mathematics 11, 1180 (2023). https://doi.org/10.3390/math1105118010.3390/math11051180 ↗
2. Adhikari, S., Karličić, D., Liu, X.: Dynamic stiffness of nonlocal damped nano-beams on elastic foundation. Eur J Mech ASolids 86, 104144 (2021). https://doi.org/10.1016/j.euromechsol.2020.10414410.1016/j.euromechsol.2020.104144 ↗
3. Alibakhshi, A., Dastjerdi, S., Malikan, M., Eremeyev, V.A.: Nonlinear free and forced vibrations of a hyperelastic micro/nanobeam considering strain stiffening effect. Nanomaterials 11, 3066 (2021). https://doi.org/10.3390/nano1111306610.3390/nano11113066 ↗
4. Ansari, R., Gholami, R., Hosseini, K., Sahmani, S.: A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory. Math. Comput. Model. 54, 2577–2586 (2011). https://doi.org/10.1016/j.mcm.2011.06.03010.1016/j.mcm.2011.06.030 ↗
5. Apuzzo, A., Barretta, R., Luciano, R., Marotti De Sciarra, F., Penna, R.: Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model. Compos. Part B Eng. 123, 105–111 (2017). https://doi.org/10.1016/j.compositesb.2017.03.05710.1016/j.compositesb.2017.03.057 ↗
6. Aria, A.I., Friswell, M.I., Rabczuk, T.: Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis. Compos. Struct. 212, 118–128 (2019). https://doi.org/10.1016/j.compstruct.2019.01.04010.1016/j.compstruct.2019.01.040 ↗
7. Aydogdu, M.: A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Phys. E Low-Dimens. Syst. Nanostruct. 41, 1651–1655 (2009). https://doi.org/10.1016/j.physe.2009.05.01410.1016/j.physe.2009.05.014 ↗
8. Bağdatlı, S.M.: Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory. Compos. Part B Eng. 80, 43–52 (2015). https://doi.org/10.1016/j.compositesb.2015.05.03010.1016/j.compositesb.2015.05.030 ↗
9. Bambaeechee, M.: Exact frequencies for free vibration of exponential and polynomial AFG beams with lumped end masses and elastic supports. J. Vib. Eng. Technol. 11, 2903–2926 (2023). https://doi.org/10.1007/s42417-022-00720-810.1007/s42417-022-00720-8 ↗
10. Bambaeechee, M.: Free vibration of AFG beams with elastic end restraints. Steel Compos. Struct. 33, 403–432 (2019). https://doi.org/10.12989/scs.2019.33.3.40310.12989/scs.2019.33.3.403 ↗
11. Bambaeechee, M.: Free transverse vibration of general power-law NAFG beams with tip masses. J. Vib. Eng. Technol. 10, 2765–2797 (2022). https://doi.org/10.1007/s42417-022-00519-710.1007/s42417-022-00519-7 ↗
12. Barretta, R., Fabbrocino, F., Luciano, R., Sciarra, F.M.D.: Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams. Phys. E Low-Dimens. Syst. Nanostruct. 97, 13–30 (2018a). https://doi.org/10.1016/j.physe.2017.09.02610.1016/j.physe.2017.09.026 ↗
13. Barretta, R., Faghidian, S.A., Luciano, R., Medaglia, C.M., Penna, R.: Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models. Compos. Part B Eng. 154, 20–32 (2018b). https://doi.org/10.1016/j.compositesb.2018.07.03610.1016/j.compositesb.2018.07.036 ↗
14. Barretta, R., Marotti De Sciarra, F.: Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams. Int. J. Eng. Sci. 130, 187–198 (2018). https://doi.org/10.1016/j.ijengsci.2018.05.00910.1016/j.ijengsci.2018.05.009 ↗
15. Behdad, S., Fakher, M., Naderi, A., Hosseini-Hashemi, S.: Vibrations of defected local/nonlocal nanobeams surrounded with two-phase Winkler-Pasternak medium: non-classic compatibility conditions and exact solution. Waves Random Complex Media (2021). https://doi.org/10.1080/17455030.2021.191879610.1080/17455030.2021.1918796 ↗
16. Behera, L., Chakraverty, S.: Application of differential quadrature method in free vibration analysis of nanobeams based on various nonlocal theories. Comput. Math. Appl. 69, 1444–1462 (2015). https://doi.org/10.1016/j.camwa.2015.04.01010.1016/j.camwa.2015.04.010 ↗
17. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T., Dihaj, A.: Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix. Struct. Eng. Mech. 67, 517–525 (2018). https://doi.org/10.12989/sem.2018.67.5.51710.12989/sem.2018.67.5.517 ↗
18. Cajić, M., Karličić, D., Lazarević, M.: Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle. Theor. Appl. Mech. 42, 167–190 (2015). https://doi.org/10.2298/TAM1503167C10.2298/TAM1503167C ↗
19. Civalek, Ö., Uzun, B., Yaylı, M.Ö., Akgöz, B.: Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method. Eur. Phys. J. plus 135, 381 (2020). https://doi.org/10.1140/epjp/s13360-020-00385-w10.1140/epjp/s13360-020-00385-w ↗
20. Darban, H., Luciano, R., Basista, M.: Calibration of the length scale parameter for the stress-driven nonlocal elasticity model from quasi-static and dynamic experiments. Mech. Adv. Mater. Struct. 30, 3518–3524 (2023). https://doi.org/10.1080/15376494.2022.207748810.1080/15376494.2022.2077488 ↗
21. De Rosa, M.A., Lippiello, M.: Nonlocal frequency analysis of embedded single-walled carbon nanotube using the Differential Quadrature Method. Compos. Part B Eng. 84, 41–51 (2016). https://doi.org/10.1016/j.compositesb.2015.08.06510.1016/j.compositesb.2015.08.065 ↗
22. De Rosa, M.A., Lippiello, M., Babilio, E., Ceraldi, C.: Nonlocal vibration analysis of a nonuniform carbon nanotube with elastic constraints and an attached mass. Mater. Basel Switz. 14, 3445 (2021). https://doi.org/10.3390/ma1413344510.3390/ma14133445 ↗
23. De Rosa, M.A., Lippiello, M., Martin, H.D., Piovan, M.T.: Nonlocal frequency analysis of nanosensors with different boundary conditions and attached distributed biomolecules: an approximate method. Acta Mech. 227, 2323–2342 (2016). https://doi.org/10.1007/s00707-016-1631-410.1007/s00707-016-1631-4 ↗
24. Demir, Ç.: Nonlocal vibration analysis for micro/nano beam on Winkler foundation via DTM. Int. J. Eng. Appl. Sci. 8, 108–118 (2016). https://doi.org/10.24107/ijeas.28151410.24107/ijeas.281514 ↗
25. Demir, Ç., Civalek, Ö.: A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos. Struct. 168, 872–884 (2017). https://doi.org/10.1016/j.compstruct.2017.02.09110.1016/j.compstruct.2017.02.091 ↗
26. Ehyaei, J., Ebrahimi, F., Salari, E.: Nonlocal vibration analysis of FG nano beams with different boundary conditions. Adv. Nano. Res. 4, 85–111 (2016). https://doi.org/10.12989/anr.2016.4.2.08510.12989/anr.2016.4.2.085 ↗
27. El-Borgi, S., Fernandes, R., Reddy, J.N.: Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation. Int. J. Non-Linear Mech. 77, 348–363 (2015). https://doi.org/10.1016/j.ijnonlinmec.2015.09.01310.1016/j.ijnonlinmec.2015.09.013 ↗
28. Ellali, M., Bouazza, M., Zenkour, A.M.: Hygrothermal vibration of FG nanobeam via nonlocal unknown integral variables secant-tangential shear deformation coupled theory with temperature-dependent material properties. Eur. J. Mech. Asolids 105, 105243 (2024). https://doi.org/10.1016/j.euromechsol.2024.10524310.1016/j.euromechsol.2024.105243 ↗
29. Eltaher, M.A., Alshorbagy, A.E., Mahmoud, F.F.: Vibration analysis of Euler-Bernoulli nanobeams by using finite element method. Appl. Math. Model. 37, 4787–4797 (2013). https://doi.org/10.1016/j.apm.2012.10.01610.1016/j.apm.2012.10.016 ↗
30. Eltaher, M.A., Khater, M.E., Emam, S.A.: A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40, 4109–4128 (2016). https://doi.org/10.1016/j.apm.2015.11.02610.1016/j.apm.2015.11.026 ↗
31. Eringen, A.C. (ed.): Nonlocal Continuum Field Theories. Springer, New York (2004)
32. Esen, I., Özarpa, C., Eltaher, M.A.: Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment. Compos. Struct. 261, 113552 (2021). https://doi.org/10.1016/j.compstruct.2021.11355210.1016/j.compstruct.2021.113552 ↗
33. Eyebe, G.J., Betchewe, G., Mohamadou, A., Kofané, T.: Nonlinear vibration of a nonlocal nanobeam resting on fractional-order viscoelastic Pasternak foundations. Fractal Fract 2, 2030021 (2018). https://doi.org/10.3390/FRACTALFRACT203002110.3390/FRACTALFRACT2030021 ↗
34. Fakher, M., Hosseini-Hashemi, S.: Vibration of two-phase local/nonlocal Timoshenko nanobeams with an efficient shear-locking-free finite-element model and exact solution. Eng. Comput. 38, 231–245 (2022). https://doi.org/10.1007/s00366-020-01058-z10.1007/s00366-020-01058-z ↗
35. Fakher, M., Rahmanian, S., Hosseini-Hashemi, S.: On the carbon nanotube mass nanosensor by integral form of nonlocal elasticity. Int. J. Mech. Sci. 150, 445–457 (2019). https://doi.org/10.1016/j.ijmecsci.2018.10.05110.1016/j.ijmecsci.2018.10.051 ↗
36. Feo, L., Lovisi, G., Penna, R.: Free vibration analysis of functionally graded nanobeams based on surface stress-driven nonlocal model. Mech. Adv. Mater. Struct. 31, 10391–10399 (2024). https://doi.org/10.1080/15376494.2023.228907910.1080/15376494.2023.2289079 ↗
37. Gartia, A.K., Chakraverty, S.: Free vibration of bi-directional functionally graded nanobeams resting on Winkler-Pasternak foundations. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01511-z10.1007/s42417-024-01511-z ↗
38. Ghannadpour, S.A.M., Mohammadi, B., Fazilati, J.: Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method. Compos. Struct. 96, 584–589 (2013). https://doi.org/10.1016/j.compstruct.2012.08.02410.1016/j.compstruct.2012.08.024 ↗
39. Ghazwani, M.H., Alnujaie, A., Tounsi, A., Van Vinh, P.: On the high-frequency analysis of exponentially graded nanobeams resting on Winkler-Pasternak foundations. J. Vib. Eng. Technol. (2024). https://doi.org/10.1007/s42417-024-01348-610.1007/s42417-024-01348-6 ↗
40. Horng, T.-L.: Analytical solution of vibration analysis on fixed-free single-walled carbon nanotube-based mass sensor. J. Surf. Eng. Mater. Adv. Technol. 2, 47–52 (2012). https://doi.org/10.4236/jsemat.2012.2100910.4236/jsemat.2012.21009 ↗
41. Islam, M.N., Salman, N., Devnath, I.: Analytical solutions for vibration of Bi-directional functionally graded nonlocal nanobeams. Results Eng. 18, 101046 (2023). https://doi.org/10.1016/j.rineng.2023.10104610.1016/j.rineng.2023.101046 ↗
42. Jafarzadeh Jazi, A., Shahriari, B., Torabi, K.: Exact closed form solution for the analysis of the transverse vibration mode of a Nano-Timoshenko beam with multiple concentrated masses. Int. J. Mech. Sci. 131–132, 728–743 (2017). https://doi.org/10.1016/j.ijmecsci.2017.08.02310.1016/j.ijmecsci.2017.08.023 ↗
43. Jena, S.K., Chakraverty, S.: Dynamic analysis of single-layered graphene nano-ribbons (SLGNRs) with variable cross-section resting on elastic foundation. Curved Layer Struct. 6, 132–145 (2019). https://doi.org/10.1515/cls-2019-001110.1515/cls-2019-0011 ↗
44. Jena, S.K., Chakraverty, S., Mahesh, V., Harursampath, D.: Wavelet-based techniques for Hygro-Magneto-Thermo vibration of nonlocal strain gradient nanobeam resting on Winkler-Pasternak elastic foundation. Eng. Anal. Bound Elem. 140, 494–506 (2022). https://doi.org/10.1016/j.enganabound.2022.04.03710.1016/j.enganabound.2022.04.037 ↗
45. Jena, S.K., Chakraverty, S., Malikan, M., Sedighi, H.: Implementation of Hermite-Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity. J. Mech. Mater. Struct. 15, 405–434 (2020). https://doi.org/10.2140/jomms.2020.15.40510.2140/jomms.2020.15.405 ↗
46. Jiang, J., Wang, L., Zhang, Y.: Vibration of single-walled carbon nanotubes with elastic boundary conditions. Int. J. Mech. Sci. 122, 156–166 (2017). https://doi.org/10.1016/j.ijmecsci.2017.01.01210.1016/j.ijmecsci.2017.01.012 ↗
47. Karmakar, S., Chakraverty, S.: Differential quadrature and Adomian decomposition methods for solving thermal vibration of Euler nanobeam resting on Winkler-Pasternak foundation. J. Mech. Mater. Struct. 16, 555–572 (2021). https://doi.org/10.2140/jomms.2021.16.55510.2140/jomms.2021.16.555 ↗
48. Khaniki, H.B., Hosseini-Hashemi, S., Khaniki, H.B.: Dynamic analysis of nano-beams embedded in a varying nonlinear elastic environment using Eringen’s two-phase local/nonlocal model. Eur. Phys. J. plus 133, 283 (2018). https://doi.org/10.1140/epjp/i2018-12128-510.1140/epjp/i2018-12128-5 ↗
49. Kiani, K.: A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect. Int. J. Mech. Sci. 52, 1343–1356 (2010). https://doi.org/10.1016/j.ijmecsci.2010.06.01010.1016/j.ijmecsci.2010.06.010 ↗
50. Kumar, Y., Ali, I.: Free vibration and buckling analyses of nanobeam embedded in Pasternak foundation. Mech. Adv. Compos. Struct. 10, 419–436 (2023). https://doi.org/10.22075/macs.2023.29904.147710.22075/macs.2023.29904.1477 ↗
51. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003). https://doi.org/10.1016/S0022-5096(03)00053-X10.1016/S0022-5096(03)00053-X ↗
52. Li, G., Xing, Y., Wang, Z., Sun, Q.: Effect of boundary conditions and constitutive relations on the free vibration of nonlocal beams. Results Phys. 19, 103414 (2020). https://doi.org/10.1016/j.rinp.2020.10341410.1016/j.rinp.2020.103414 ↗
53. Li, X.-F., Tang, G.-J., Shen, Z.-B., Lee, K.Y.: Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55, 75–84 (2015). https://doi.org/10.1016/j.ultras.2014.08.00210.1016/j.ultras.2014.08.002 ↗
54. Loghmani, M., Hairi Yazdi, M.R.: An analytical method for free vibration of multi cracked and stepped nonlocal nanobeams based on wave approach. Results Phys. 11, 166–181 (2018). https://doi.org/10.1016/j.rinp.2018.08.04610.1016/j.rinp.2018.08.046 ↗
55. Lovisi, G., Feo, L., Lambiase, A., Penna, R.: Application of surface stress-driven model for higher vibration modes of functionally graded nanobeams. Nanomaterials 14, 350 (2024). https://doi.org/10.3390/nano1404035010.3390/nano14040350 ↗
56. Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Dynamic properties of flexural beams using a nonlocal elasticity model. J. Appl. Phys. 99, 073510 (2006). https://doi.org/10.1063/1.218921310.1063/1.2189213 ↗
57. Lu, P., Lee, H.P., Lu, C., Zhang, P.Q.: Application of nonlocal beam models for carbon nanotubes. Int. J. Solids Struct. 44, 5289–5300 (2007). https://doi.org/10.1016/j.ijsolstr.2006.12.03410.1016/j.ijsolstr.2006.12.034 ↗
58. Malikan, M., Dimitri, R., Tornabene, F.: Transient response of oscillated carbon nanotubes with an internal and external damping. Compos. Part B Eng. 158, 198–205 (2019). https://doi.org/10.1016/j.compositesb.2018.09.09210.1016/j.compositesb.2018.09.092 ↗
59. Malikan, M., Eremeyev, V.A.: Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method. Mater. Res. Express 7, 025005 (2020). https://doi.org/10.1088/2053-1591/ab691c10.1088/2053-1591/ab691c ↗
60. Malikan, M., Nguyen, V.B., Tornabene, F.: Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Eng. Sci. Technol. Int. J. 21, 778–786 (2018). https://doi.org/10.1016/j.jestch.2018.06.00110.1016/j.jestch.2018.06.001 ↗
61. Mamu, R.M., Togun, N.: Thermal effects on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic medium. Acta Mech. (2024). https://doi.org/10.1007/s00707-024-03894-210.1007/s00707-024-03894-2 ↗
62. Mehdipour, I., Barari, A., Domairry, G.: Application of a cantilevered SWCNT with mass at the tip as a nanomechanical sensor. Comput. Mater. Sci. 50, 1830–1833 (2011). https://doi.org/10.1016/j.commatsci.2011.01.02510.1016/j.commatsci.2011.01.025 ↗
63. Mohamed, S.A., Gamal, L., Shanab, R.A., Eraky Bakry, A.: A comparison of FEM and DIQM in investigating the nonlinear free vibration of axially functionally graded tapered microbeams with general boundary conditions. Compos. Struct. 282, 115027 (2022). https://doi.org/10.1016/j.compstruct.2021.11502710.1016/j.compstruct.2021.115027 ↗
64. Moutlana, M.K., Adali, S.: Effects of elastic restraints on the fundamental frequency of nonlocal nanobeams with tip mass. Int. J. Acoust. Vib. 24, 520–530 (2019). https://doi.org/10.20855/ijav.2019.24.3136810.20855/ijav.2019.24.31368 ↗
65. Murmu, T., Adhikari, S.: Nonlocal frequency analysis of nanoscale biosensors. Sens. Actuators Phys. 173, 41–48 (2012). https://doi.org/10.1016/j.sna.2011.10.01210.1016/j.sna.2011.10.012 ↗
66. Murmu, T., Pradhan, S.C.: Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Comput. Mater. Sci. 46, 854–859 (2009). https://doi.org/10.1016/j.commatsci.2009.04.01910.1016/j.commatsci.2009.04.019 ↗
67. Mustapha, K.B., Zhong, Z.W.: Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium. Comput. Mater. Sci. 50, 742–751 (2010). https://doi.org/10.1016/j.commatsci.2010.10.00510.1016/j.commatsci.2010.10.005 ↗
68. Najafi, M., Ahmadi, I.: A nonlocal Layerwise theory for free vibration analysis of nanobeams with various boundary conditions on Winkler-Pasternak foundation. Steel Compos. Struct. 40, 101–119 (2021). https://doi.org/10.12989/scs.2021.40.1.10110.12989/scs.2021.40.1.101 ↗
69. Nazemnezhad, R., Hosseini Hashemi, S.: Nonlocal nonlinear free vibration of functionally graded nanobeams. Compos. Struct. 110, 192–199 (2014). https://doi.org/10.1016/j.compstruct.2013.12.00610.1016/j.compstruct.2013.12.006 ↗
70. Nešić, N., Cajić, M., Karličić, D., Obradović, A., Simonović, J.: Nonlinear vibration of a nonlocal functionally graded beam on fractional visco-Pasternak foundation. Nonlinear Dyn. 107, 2003–2026 (2022). https://doi.org/10.1007/s11071-021-07081-z10.1007/s11071-021-07081-z ↗
71. Niknam, H., Aghdam, M.M.: A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation. Compos. Struct. 119, 452–462 (2015). https://doi.org/10.1016/j.compstruct.2014.09.02310.1016/j.compstruct.2014.09.023 ↗
72. Numanoğlu, H.M., Ersoy, H., Civalek, O., Ferreira, A.J.M.: Derivation of nonlocal FEM formulation for thermo-elastic Timoshenko beams on elastic matrix. Compos. Struct. 273, 114292 (2021). https://doi.org/10.1016/j.compstruct.2021.11429210.1016/j.compstruct.2021.114292 ↗
73. Peddieson, J., Buchanan, G.R., McNitt, R.P.: Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci. 41, 305–312 (2003). https://doi.org/10.1016/S0020-7225(02)00210-010.1016/S0020-7225(02)00210-0 ↗
74. Penna, R., Feo, L., Lovisi, G., Fabbrocino, F.: Application of the higher-order Hamilton approach to the nonlinear free vibrations analysis of porous FG nano-beams in a hygrothermal environment based on a local/nonlocal stress gradient model of elasticity. Nanomaterials 12, 2098 (2022). https://doi.org/10.3390/nano1212209810.3390/nano12122098 ↗
75. Rahmanian, M., Torkaman-Asadi, M.A., Firouz-Abadi, R.D., Kouchakzadeh, M.A.: Free vibrations analysis of carbon nanotubes resting on Winkler foundations based on nonlocal models. Phys. B Condens. Matter. 484, 83–94 (2016). https://doi.org/10.1016/j.physb.2015.12.04110.1016/j.physb.2015.12.041 ↗
76. Reddy, J.N.: Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007). https://doi.org/10.1016/j.ijengsci.2007.04.00410.1016/j.ijengsci.2007.04.004 ↗
77. Refaeinejad, V., Rahmani, O., Hosseini, S.A.H.: An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories. Sci. Iran 24, 1635–1653 (2017). https://doi.org/10.24200/sci.2017.414110.24200/sci.2017.4141 ↗
78. Romano, G., Barretta, R.: Stress-driven versus strain-driven nonlocal integral model for elastic nano-beams. Compos. Part B Eng. 114, 184–188 (2017a). https://doi.org/10.1016/j.compositesb.2017.01.00810.1016/j.compositesb.2017.01.008 ↗
79. Romano, G., Barretta, R.: Nonlocal elasticity in nanobeams: the stress-driven integral model. Int. J. Eng. Sci. 115, 14–27 (2017b). https://doi.org/10.1016/j.ijengsci.2017.03.00210.1016/j.ijengsci.2017.03.002 ↗
80. Romano, G., Barretta, R., Diaco, M., Marotti De Sciarra, F.: Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams. Int. J. Mech. Sci. 121, 151–156 (2017). https://doi.org/10.1016/j.ijmecsci.2016.10.03610.1016/j.ijmecsci.2016.10.036 ↗
81. Shi, Z., Yao, X., Pang, F., Wang, Q.: An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions. Sci. Rep. 7, 12909 (2017). https://doi.org/10.1038/s41598-017-12596-w10.1038/s41598-017-12596-w ↗
82. Siddique, M.U.M., Islam, M.N., Devnath, I.: Analytical solutions for bending, buckling and vibration of nanobeams on Winkler-Pasternak foundation. Int. J. Comput. Mater. Sci. Eng. 12, 2250020 (2023). https://doi.org/10.1142/S204768412250020810.1142/S2047684122500208 ↗
83. Şimşek, M.: Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory. Compos. Part B Eng. 56, 621–628 (2014). https://doi.org/10.1016/j.compositesb.2013.08.08210.1016/j.compositesb.2013.08.082 ↗
84. Şimşek, M.: 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 (2019). https://doi.org/10.1016/j.compstruct.2019.11104110.1016/j.compstruct.2019.111041 ↗
85. Taima, M.S., El-Sayed, T.A., Farghaly, S.H.: Free vibration analysis of multistepped nonlocal Bernoulli-Euler beams using dynamic stiffness matrix method. J. Vib. Control 27, 774–789 (2021). https://doi.org/10.1177/107754632093347010.1177/1077546320933470 ↗
86. Taima, M.S., El-Sayed, T.A., Friswell, M.I.: Thermal vibration analysis of cracked nanobeams submerged in elastic foundations by nonlocal continuum mechanics. Thin-Walled Struct. 193, 111249 (2023). https://doi.org/10.1016/j.tws.2023.11124910.1016/j.tws.2023.111249 ↗
87. Togun, N.: Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory. Microsyst. Technol. 22, 2349–2359 (2016a). https://doi.org/10.1007/s00542-016-3062-510.1007/s00542-016-3062-5 ↗
88. Togun, N.: Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation. Bound Value Probl. 2016, 57 (2016b). https://doi.org/10.1186/s13661-016-0561-310.1186/s13661-016-0561-3 ↗
89. Togun, N., Bağdatlı, S.M.: Nonlinear vibration of a nanobeam on a Pasternak elastic foundation based on non-local Euler-Bernoulli beam theory. Math. Comput. Appl. 21, 3 (2016). https://doi.org/10.3390/mca2101000310.3390/mca21010003 ↗
90. Trabelssi, M., El-Borgi, S., Ke, L.-L., Reddy, J.N.: Nonlocal free vibration of graded nanobeams resting on a nonlinear elastic foundation using DQM and LaDQM. Compos. Struct. 176, 736–747 (2017). https://doi.org/10.1016/j.compstruct.2017.06.01010.1016/j.compstruct.2017.06.010 ↗
91. Tuna, M., Kirca, M.: Exact solution of Eringen’s nonlocal integral model for vibration and buckling of Euler-Bernoulli beam. Int. J. Eng. Sci. 107, 54–67 (2016). https://doi.org/10.1016/j.ijengsci.2016.07.00410.1016/j.ijengsci.2016.07.004 ↗
92. Tuna, M., Kirca, M.: Bending, buckling and free vibration analysis of Euler-Bernoulli nanobeams using Eringen’s nonlocal integral model via finite element method. Compos. Struct. 179, 269–284 (2017). https://doi.org/10.1016/j.compstruct.2017.07.01910.1016/j.compstruct.2017.07.019 ↗
93. Uzun, B., Civalek, Ö.: Free vibration analysis Silicon nanowires surrounded by elastic matrix by nonlocal finite element method. Adv Nano Res 7, 99–108 (2019). https://doi.org/10.12989/anr.2019.7.2.09910.12989/anr.2019.7.2.099 ↗
94. Uzun, B., Civalek, Ö., Yaylı, M.Ö.: Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mech. Based des. Struct. Mach. 51, 481–500 (2023a). https://doi.org/10.1080/15397734.2020.184656010.1080/15397734.2020.1846560 ↗
95. Uzun, B., Civalek, Ö., Yaylı, M.Ö.: A hardening nonlocal approach for vibration of axially loaded nanobeam with deformable boundaries. Acta Mech. 234, 2205–2222 (2023b). https://doi.org/10.1007/s00707-023-03490-w10.1007/s00707-023-03490-w ↗
96. Uzun, B., Yayli, M.Ö.: Porosity and deformable boundary effects on the dynamic of nonlocal sigmoid and power-law FG nanobeams embedded in the Winkler-Pasternak medium. J. Vib. Eng. Technol. (2023). https://doi.org/10.1007/s42417-023-01039-810.1007/s42417-023-01039-8 ↗
97. Uzun, B., Yaylı, M.Ö.: Nonlocal vibration analysis of Ti-6Al-4V/ZrO2 functionally graded nanobeam on elastic matrix. Arab. J. Geosci. 13, 155 (2020). https://doi.org/10.1007/s12517-020-5168-410.1007/s12517-020-5168-4 ↗
98. Uzun, B., Yaylı, M.Ö.: Free vibration of a carbon nanotube-reinforced nanowire/nanobeam with movable ends. J. Vib. Eng. Technol. 12, 6847–6863 (2024). https://doi.org/10.1007/s42417-024-01287-210.1007/s42417-024-01287-2 ↗
99. Wang, C.M., Zhang, H., Challamel, N., Duan, W.H.: Eringen’s small length scale coefficient for vibration of axially loaded nonlocal Euler beams with elastic end restraints. J. Model Mech. Mater. (2017). https://doi.org/10.1515/jmmm-2016-015810.1515/jmmm-2016-0158 ↗
100. Wang, C.M., Zhang, Y.Y., He, X.Q.: Vibration of nonlocal Timoshenko beams. Nanotechnology 18, 105401 (2007). https://doi.org/10.1088/0957-4484/18/10/10540110.1088/0957-4484/18/10/105401 ↗