Double functionally graded porous resonator combining hollow microcore via nonlocal strain gradient approach for large adsorption of water molecules
Bibliographic record
Abstract
No abstract is available for this record. The assistant can identify its topic from the title, but cannot infer the study’s results.
Source: Not provided · Quality: missing
Research context
OpenAlex topics: Nonlocal and gradient elasticity in micro/nano structures · Acoustic Wave Resonator Technologies · Advanced Materials and Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (100+)
Show source-provided references
1. Abdelrahman, A.A., Esen, I., Özarpa, C., Eltaher, M.A.: Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory. Appl. Math. Model. 96, 215–235 (2021). https://doi.org/10.1016/j.apm.2021.03.00810.1016/j.apm.2021.03.008 ↗
2. Abdelrahman, A. A., Saleem, H. A., Abdelhaffez, G. S., Eltaher, M. A.: On bending of piezoelectrically layered perforated nanobeams embedded in an elastic foundation with flexoelectricity. Mathematics 11(5), Article 5 (2023). https://doi.org/10.3390/math1105116210.3390/math11051162 ↗
3. Adali, S.: Variational principles for a double Rayleigh beam system undergoing vibrations and connected by a nonlinear Winkler-Pasternak elastic layer. Nonlinear Eng. (2022). https://doi.org/10.1515/nleng-2022-025910.1515/nleng-2022-0259 ↗
4. Allam, M.N., Radwan, A.F.: Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium. Adv. Mech. Eng. 11(4), 1687814019837067 (2019). https://doi.org/10.1177/168781401983706710.1177/1687814019837067 ↗
5. Alshenawy, R., Safaei, B., Sahmani, S., Elmoghazy, Y., Al-Alwan, A., Nuwairan, M.A.: Buckling mode transition in nonlinear strain gradient-based stability behavior of axial-thermal-electrical loaded FG piezoelectric cylindrical panels at microscale. Eng. Anal. Bound. Elem. 141, 36–64 (2022). https://doi.org/10.1016/j.enganabound.2022.04.01010.1016/j.enganabound.2022.04.010 ↗
6. Al-Shujairi, M., Mollamahmutoğlu, Ç.: Dynamic stability of sandwich functionally graded micro-beam based on the nonlocal strain gradient theory with thermal effect. Comp. Struct. 201, 1018–1030 (2018). https://doi.org/10.1016/j.compstruct.2018.06.03510.1016/j.compstruct.2018.06.035 ↗
7. Amir, M., Lim, J., Kim, S.-W., Lee, S.-Y.: Finite element analysis of natural frequencies of the FGM porous cooling plate with cutouts: a multilayered FGM approach. Results Eng. 20, 101532 (2023). https://doi.org/10.1016/j.rineng.2023.10153210.1016/j.rineng.2023.101532 ↗
8. 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(11), 2577–2586 (2011). https://doi.org/10.1016/j.mcm.2011.06.03010.1016/j.mcm.2011.06.030 ↗
9. Attia, M.A., Matbuly, M.S., Osman, T., AbdElkhalek, M.: Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method. Acta Mech. 235, 1961–2012 (2024). https://doi.org/10.1007/s00707-023-03797-810.1007/s00707-023-03797-8 ↗
10. Avcar, M., Alsaid Alwan, H.: Free vibration of functionally graded Rayleigh beam. Int. J. Eng. Appl. Sci., 9, 127–127 (2017). https://doi.org/10.24107/ijeas.32288410.24107/ijeas.322884 ↗
11. Aydogdu, M., Taskin, V.: Free vibration analysis of functionally graded beams with simply supported edges. Mater. des. 28(5), 1651–1656 (2007). https://doi.org/10.1016/j.matdes.2006.02.00710.1016/j.matdes.2006.02.007 ↗
12. Baetens, T., Arscott, S.: Planarization and edge bead reduction of spin-coated polydimethylsiloxane. J. Micromech. Microeng., 29 (2019). https://doi.org/10.1088/1361-6439/ab3b1810.1088/1361-6439/ab3b18 ↗
13. Belkhodja, M.E.A., Chorfi, S.M., Belalia, S.A., Belkhodja, Y.: Bending and free vibrations analysis of sandwich beams with porous functionally graded face sheets and a graphene platelets-reinforced aluminum core using a new quasi-3D beam theory. J. Vib. Eng. Technol. 13(1), 122 (2025). https://doi.org/10.1007/s42417-024-01646-z10.1007/s42417-024-01646-z ↗
14. Bertram, A., Forest, S. (eds.): Mechanics of Strain Gradient Materials. Springer, Cham (2020)
15. Berg, A., Peter, C., Johnston, K.: Evaluation and optimization of interface force fields for water on gold surfaces. J. Chem. Theory Comput. 13, 5610–5623 (2017). https://doi.org/10.1021/acs.jctc.7b0061210.1021/acs.jctc.7b00612 ↗
16. Bourouina, H., Boussendel, A.: Theoretical Prediction of proteins network-induced nonlocal response in molecules-resonator biosensor with Hydrogen bonds including van der Waals interactions. Phys. Scr., 99 (2024). https://doi.org/10.1088/1402-4896/ad23af10.1088/1402-4896/ad23af ↗
17. Bourouina, H., Derguini, N., Yahiaoui, R.: Coupling spring-induced resonance shift in PDNB system with PSH network. Microsyst. Technol. 29, 91–106 (2023). https://doi.org/10.1007/s00542-022-05393-710.1007/s00542-022-05393-7 ↗
18. Bourouina, H., Yahiaoui, R., Kerid, R., Benamar, M., Brioua, F.: Adsorption-induced nonlocal frequency shift in adatoms-nanobeam system. Phys. B Condens. Matter., 520 (2017). https://doi.org/10.1016/j.physb.2017.06.01210.1016/j.physb.2017.06.012 ↗
19. Bourouina, H., Yahiaoui, R., Kerid, R., Ghoumid, K., Lajoie, I., Picaud, F., Herlem, G.: The influence of hole networks on the adsorption-induced frequency shift of a perforated nanobeam using non-local elasticity theory. J. Phys. Chem. Solids 136, 109201 (2020). https://doi.org/10.1016/j.jpcs.2019.10920110.1016/j.jpcs.2019.109201 ↗
20. Bourouina, H., Yahiaoui, R., Sahar, A., Benamar, M.E.A.: Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads. Phys. E Low Dim. Syst. Nanostruct. 75, 163–168 (2016). https://doi.org/10.1016/j.physe.2015.09.01410.1016/j.physe.2015.09.014 ↗
21. Brahma, L., Guha, K., Karumuri, S.R.: Design and analysis of novel MEMS cantilever biosensor with special focus on SCR for tuberculosis detection. Microsyst. Technol. 31(2), 353–366 (2025). https://doi.org/10.1007/s00542-024-05689-w10.1007/s00542-024-05689-w ↗
22. Chawla, R., Pakrashi, V.: Dynamic responses of a damaged double Euler-Bernoulli beam traversed by a ‘phantom’ vehicle. Struct. Control. Health Monit. 29, e2933 (2022). https://doi.org/10.1002/stc.293310.1002/stc.2933 ↗
23. Chen, D., Yang, J., Kitipornchai, S.: Elastic buckling and static bending of shear deformable functionally graded porous beam. Compos. Struct. 133, 54–61 (2015). https://doi.org/10.1016/j.compstruct.2015.07.05210.1016/j.compstruct.2015.07.052 ↗
24. Chen, D., Wang, Y., Zheng, S., Liang, Y., Sun, S.: Isogeometric analysis of bi-directional functionally graded porous micro-beam with geometrical imperfections using nonlocal strain gradient theory. J. Vib. Eng. Technol. 12(1), 1031–1043 (2024). https://doi.org/10.1007/s42417-024-01460-710.1007/s42417-024-01460-7 ↗
25. Chen, G.Y., Thundat, T., Wachter, E.A., Warmack, R.J.: Adsorption-induced surface stress and its effects on resonant frequency of microcantilevers. J. Appl. Phys. 77, 3618–3622 (1995). https://doi.org/10.1063/1.35956210.1063/1.359562 ↗
26. Chen, S.-X., Sahmani, S., Safaei, B.: Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling. Eng. Comput. 37(2), 1657–1678 (2021). https://doi.org/10.1007/s00366-021-01303-z10.1007/s00366-021-01303-z ↗
27. Chen, S., Zhang, Q., Liu, H.: Dynamic response of double-FG porous beam system subjected to moving load. Eng. Comput. 38(S3), 2309–2328 (2022). https://doi.org/10.1007/s00366-021-01376-w10.1007/s00366-021-01376-w ↗
28. Coleman, M.P., McSweeney, L.A.: The exact frequency equations for the Rayleigh and shear beams with boundary damping. Int. J. Acoust. Vib. 25 (1), 3–8 (2020). https://doi.org/10.20855/ijav.2020.25.1142210.20855/ijav.2020.25.11422 ↗
29. Dang, V.-H., Nguyen, D.-A., Le, M.-Q., Duong, T.-H.: Nonlinear vibration of nanobeams under electrostatic force based on the nonlocal strain gradient theory. Int. J. Mech. Mater. des. 16(2), 289–308 (2020). https://doi.org/10.1007/s10999-019-09468-810.1007/s10999-019-09468-8 ↗
30. Du, B., Xu, F., & Fen, Z.: Impacts of complex fields and surface energy on forced and free vibrations of Rayleigh nanobeams under a traveling load. J. Vib. Eng. Technol. 12, (2023). https://doi.org/10.1007/s42417-023-01154-610.1007/s42417-023-01154-6 ↗
31. Ebrahimi, F., Daman, M., & Mahesh, V.: Thermo-mechanical vibration analysis of curved imperfect nano-beams based on nonlocal strain gradient theory. Adv. Nano Res. 7(4), 249–263 (2019). https://doi.org/10.12989/anr.2019.7.4.24910.12989/anr.2019.7.4.249 ↗
32. Ebrahimi-Mamaghani, A., Sarparast, H., Rezaei, M.: On the vibrations of axially graded Rayleigh beams under a moving load. Appl. Math. Model. 84, 554–570 (2020). https://doi.org/10.1016/j.apm.2020.04.00210.1016/j.apm.2020.04.002 ↗
33. Elaikh, T.E.H., Abd, N.M., Ali, A.H.: Dynamic characteristics of cracked simply supported bidirectional functionally graded Rayleigh beam. Results Mater. 19, 100441 (2023). https://doi.org/10.1016/j.rinma.2023.10044110.1016/j.rinma.2023.100441 ↗
34. Elshabrawy, M., Abdeen, M., Nassar, M., Bakr, O., Abbas, W.: Analysis of tapered timoshenko and Euler-Bernoulli beams on an elastic foundation with moving loads. J. Math. 2021, 6616707 (2021). https://doi.org/10.1155/2021/661670710.1155/2021/6616707 ↗
35. Eltaher, M. A., Fouda, N., El-Midany, T., & Sadoun, A.: Modified porosity model in analysis of functionally graded porous nanobeams. J. Braz. Soc. Mech. Sci. Eng. 40, (2018). https://doi.org/10.1007/s40430-018-1065-010.1007/s40430-018-1065-0 ↗
36. Eringen, A.C.: Linear theory of nonlocal elasticity and dispersion of plane waves. Int. J. Eng. Sci. 10(5), 425–435 (1972). https://doi.org/10.1016/0020-7225(72)90050-X10.1016/0020-7225(72)90050-X ↗
37. Eringen, A.C. (ed.): Nonlocal continuum field theories. Springer, New York, NY (2002)
38. Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983). https://doi.org/10.1063/1.33280310.1063/1.332803 ↗
39. Esen, İ., Abdelrahman, A., & Eltaher, M. A.: Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields. Eng. Comput. 38, (2022). https://doi.org/10.1007/s00366-021-01389-510.1007/s00366-021-01389-5 ↗
40. Esen, I., Abdelrahman, A.A., Eltaher, M.A.: On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load. Int. J. Mech. Mater. des. 17(3), 721–742 (2021a). https://doi.org/10.1007/s10999-021-09555-910.1007/s10999-021-09555-9 ↗
41. 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 (2021b). https://doi.org/10.1016/j.compstruct.2021.11355210.1016/j.compstruct.2021.113552 ↗
42. Fan, F., Sahmani, S., Safaei, B.: Nonlocal strain gradient-based nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric multilayer energy nanoharvesters. Polym. Compos. 45(3), 2080–2100 (2024). https://doi.org/10.1002/pc.2790510.1002/pc.27905 ↗
43. Farokhi, H., Ghayesh, M.H., Gholipour, A.: Dynamics of functionally graded micro-cantilevers. Int. J. Eng. Sci. 115, 117–130 (2017). https://doi.org/10.1016/j.ijengsci.2017.01.00410.1016/j.ijengsci.2017.01.004 ↗
44. Farajpour, A., Rastgoo, A.: Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory. Results Phys. 7, 1367–1375 (2017). https://doi.org/10.1016/j.rinp.2017.03.03810.1016/j.rinp.2017.03.038 ↗
45. Feizi, S., Cooksley, C.M., Nepal, R., Psaltis, A.J., Wormald, P.-J., Vreugde, S.: Silver nanoparticles as a bioadjuvant of antibiotics against biofilm-mediated infections with methicillin-resistant Staphylococcus aureus and Pseudomonas aeruginosa in chronic rhinosinusitis patients. Pathology 54(4), 453–459 (2022). https://doi.org/10.1016/j.pathol.2021.08.01410.1016/j.pathol.2021.08.014 ↗
46. Firouzi, N., Alzaidi, A.S.M., Nezaminia, H., Dalalchi, D.: Numerical investigation on effect of different parameters on nonlinear vibration response of fully geometrically exact Timoshenko beams. Appl. Phys. A 130(9), 618 (2024). https://doi.org/10.1007/s00339-024-07775-210.1007/s00339-024-07775-2 ↗
47. Firouzi, N., Dohnal, F., Gorbach, T., Farizeh, T.: Experimental and numerical analysis of nonlinear velocity response for a cantilever. Int. J. Non Linear Mech. 173, 105067 (2025). https://doi.org/10.1016/j.ijnonlinmec.2025.10506710.1016/j.ijnonlinmec.2025.105067 ↗
48. Fu, G., Zhou, S., Qi, L.: A size-dependent Bernoulli-Euler beam model based on strain gradient elasticity theory incorporating surface effects. ZAMM J. Appl. Math. Mech. 99(6), e201800048 (2019). https://doi.org/10.1002/zamm.20180004810.1002/zamm.201800048 ↗
49. Gbadeyan, J.A., Hammed, F.A.: Influence of a moving mass on the dynamic behaviour of viscoelastically connected prismatic double Rayleigh beam system having arbitrary end supports. Chin. J. Math. 2017, 6058035 (2017). https://doi.org/10.1155/2017/605803510.1155/2017/6058035 ↗
50. Ghayesh, M.H., Farajpour, A.: A review on the mechanics of functionally graded nanoscale and microscale structures. Int. J. Eng. Sci. 137, 8–36 (2019). https://doi.org/10.1016/j.ijengsci.2018.12.00110.1016/j.ijengsci.2018.12.001 ↗
51. Gheshlaghi, B., Hasheminejad, S.: Adsorption-induced resonance frequency shift in Timoshenko microbeams. Curr. Appl. Phys. 11, 1035–1041 (2011). https://doi.org/10.1016/j.cap.2011.01.02510.1016/j.cap.2011.01.025 ↗
52. Gholami, M., Zare, E., Alibazi, A.: Applying Eringen’s nonlocal elasticity theory for analyzing the nonlinear free vibration of bidirectional functionally graded Euler–Bernoulli nanobeams. Arch. Appl. Mech. 91, (2021). https://doi.org/10.1007/s00419-021-01939-910.1007/s00419-021-01939-9 ↗
53. Ghommem, M., Abdelkefi, A.: Nonlinear reduced-order modeling and effectiveness of electrically-actuated microbeams for bio-mass sensing applications. Int. J. Mech. Mater. des. 15(1), 125–143 (2019). https://doi.org/10.1007/s10999-018-9402-010.1007/s10999-018-9402-0 ↗
54. Guerroudj, M., Drai, A., Daikh, A.A., et al.: Size-dependent free vibration analysis of multidirectional functionally graded nanobeams via a nonlocal strain gradient theory. J. Eng. Math. 146, 20 (2024). https://doi.org/10.1007/s10665-024-10373-z10.1007/s10665-024-10373-z ↗
55. Guo, L., Xin, X., Shahsavari, D., Karami, B.: Dynamic response of porous E-FGM thick microplate resting on elastic foundation subjected to moving load with acceleration. Thin-Walled Struct. 173, 108981 (2022). https://doi.org/10.1016/j.tws.2022.10898110.1016/j.tws.2022.108981 ↗
56. Hajjaj, A.Z., Ortiz, J., Abdelkefi, A.: Nonlinear size-dependent modeling and dynamics of nanocrystalline arc resonators. Int. J. Mech. Mater. des. 18, 105–123 (2022). https://doi.org/10.1007/s10999-021-09574-610.1007/s10999-021-09574-6 ↗
57. Hamed, M.A., Mohamed, N.A., Eltaher, M.A.: Stability buckling and bending of nanobeams including cutouts. Eng. Comput. 38(1), 209–230 (2022). https://doi.org/10.1007/s00366-020-01063-210.1007/s00366-020-01063-2 ↗
58. Hashemian, M., Foroutan, S., Toghraie, D.: Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects. Mech. Mater., p 103209 (2019). https://doi.org/10.1016/j.mechmat.2019.10320910.1016/j.mechmat.2019.103209 ↗
59. Hassanali, A. A., Singer, S. J.: Static and dynamic properties of the water/amorphous silica interface: a model for the undissociated surface. J. Comput.-Aided Mater. Des., 14, 53–63 (2007). https://doi.org/10.1007/s10820-006-9038-510.1007/s10820-006-9038-5 ↗
60. Hassannejad, R., Alizadeh-Hamidi, B.: Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects. Int. J. Mech. Mater. des. 20, 1147–1162 (2024). https://doi.org/10.1007/s10999-024-09720-w10.1007/s10999-024-09720-w ↗
61. Hosseini, S. M. J., Torabi, J., Ansari, R.: Geometrically nonlinear nonlocal strain gradient vibration of FG shear deformable curved nanobeams. Waves Random Complex Media, pp 1–24 (2023). https://doi.org/10.1080/17455030.2022.210269110.1080/17455030.2022.2102691 ↗
62. Jacobson, D.W., Thompson, G.B.: Revisiting Lennard-Jones, Morse, and N-M potentials for metals. Comput. Mater. Sci. 205, 111206 (2022). https://doi.org/10.1016/j.commatsci.2022.11120610.1016/j.commatsci.2022.111206 ↗
63. Jankowski, P., Żur, K.K., Farajpour, A.: Analytical and meshless DQM approaches to free vibration analysis of symmetric FGM porous nanobeams with piezoelectric effect. Eng. Anal. Bound. Elem. 136, 266–289 (2022). https://doi.org/10.1016/j.enganabound.2022.01.00710.1016/j.enganabound.2022.01.007 ↗
64. 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(3), 405–434 (2020). https://doi.org/10.2140/jomms.2020.15.40510.2140/jomms.2020.15.405 ↗
65. Jimoh, A., Ajoge, E.O.: Effect of rotatory inertia and load natural frequency on the response of uniform Rayleigh beam resting on Pasternak foundation subjected to a harmonic magnitude moving load.Appl. Math. Sci., 12(16), 783–795 (2018). https://doi.org/10.12988/ams.2018.834510.12988/ams.2018.8345 ↗
66. Kafkas, U.: On the free vibration of a perforated Rayleigh beam with deformable ends. Eng. Sci. Technol. Int. J., p. 101787 (2024). https://doi.org/10.1016/j.jestch.2024.10178710.1016/j.jestch.2024.101787 ↗
67. Karami, B., Ghayesh, M.H.: Non-linear mechanics of geometrically imperfect graphene origami-enabled auxetic metamaterial third-order beam structures. Int. J. Non Linear Mech. 172, 105047 (2025). https://doi.org/10.1016/j.ijnonlinmec.2025.10504710.1016/j.ijnonlinmec.2025.105047 ↗
68. Karami, B., Ghayesh, M.H., Fantuzzi, N., Żur, K.K.: Free vibrations of higher-order quasi-3D viscoelastic bi-directional functionally graded plates. Compos. Struct. 359, 118972 (2025). https://doi.org/10.1016/j.compstruct.2025.11897210.1016/j.compstruct.2025.118972 ↗
69. Karami, B., Ghayesh, M., Hussain, S., Amabili, M.: On the size-dependent vibrations of doubly-curved porous shear deformable FGM microshells. Int. J. Mech. Syst. Dyn. (2024). https://doi.org/10.1002/msd2.1213710.1002/msd2.12137 ↗
70. Karami, B., Janghorban, M.: Numerical study on the static bending and forced vibration of triclinic plate with arbitrary boundary conditions. Arch. Civ. Mech. Eng. 23(4), 228 (2023). https://doi.org/10.1007/s43452-023-00728-110.1007/s43452-023-00728-1 ↗
71. Karami, B., Janghorban, M., Rabczuk, T.: Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory. Compos. B Eng. 182, 107622 (2020). https://doi.org/10.1016/j.compositesb.2019.10762210.1016/j.compositesb.2019.107622 ↗
72. Karimi, M., Khoshgoftar, M.J., Karimi, M., Mirzaali, M.J., Javanbakht, Z.: An analytical model for the static behaviour of honeycomb sandwich plates with auxetic cores using higher-order shear deformation theories. Int. J. Mech. Mater. des. 19(4), 951–969 (2023). https://doi.org/10.1007/s10999-023-09667-410.1007/s10999-023-09667-4 ↗
73. Kerid, R., Bourouina, H., Yahiaoui, R., Bounekhla, M., Aissat, A.: Magnetic field effect on nonlocal resonance frequencies of structure-based filter with periodic square holes network. Phys. e Low Dimen. Syst. Nanostruct. 105, 83–89 (2019). https://doi.org/10.1016/j.physe.2018.05.02110.1016/j.physe.2018.05.021 ↗
74. Khabaz, M.K., Eftekhari, S.A., Toghraie, D.: Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects. Appl. Math. Comput. 419, 126867 (2022). https://doi.org/10.1016/j.amc.2021.12686710.1016/j.amc.2021.126867 ↗
75. Khouni, S., Bourouina, H.: Nonlocal FG porous adsorber with 2D PSH network under magnetic intensity for large frequency range considering vdW interaction potentials. Phys. Scr. 99(10), 105919 (2024). https://doi.org/10.1088/1402-4896/ad72b510.1088/1402-4896/ad72b5 ↗
76. Kim, K., Han, P., Jong, K., Jang, C., Kim, R.: Natural frequency calculation of elastically connected double-beam system with arbitrary boundary condition. AIP Adv. 10, 055026 (2020). https://doi.org/10.1063/5.001098410.1063/5.0010984 ↗
77. Kim, J., Żur, K.K., Reddy, J.N.: Bending, free vibration, and buckling of modified couple stress-based functionally graded porous micro-plates. Compos. Struct. 209, 879–888 (2019). https://doi.org/10.1016/j.compstruct.2018.11.02310.1016/j.compstruct.2018.11.023 ↗
78. Koç, M.A., Eroğlu, M., Esen, İ: Dynamic analysis of high-speed train moving on perforated Timoshenko and Euler-Bernoulli beams. Int. J. Mech. Mater. des. 18(4), 893–917 (2022). https://doi.org/10.1007/s10999-022-09610-z10.1007/s10999-022-09610-z ↗
79. Lamari, A., Bourouina, H.: Nonlocal vibration response of double FG porous microbeams adsorber with 2D PSH network under magnetic intensity for large frequency range. J. Vib. Eng. Technol. 13, 38 (2025). https://doi.org/10.1007/s42417-024-01571-110.1007/s42417-024-01571-1 ↗
80. Lezgy-Nazargah, M., Trinh, L. C., Wattanasakulpong, N., Vo, T. P.: Finite element model for stability and vibration analyses of bi-directional FG curved sandwich beams. *Int. J. Mech. Mater. Des., 20(4), 849–875 (2024). https://doi.org/10.1007/s10999-023-09700-610.1007/s10999-023-09700-6 ↗
81. Li, L., Hu, Y.: Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 107, 77–97 (2016). https://doi.org/10.1016/j.ijengsci.2016.07.01110.1016/j.ijengsci.2016.07.011 ↗
82. Li, L., Hu, Y.: Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects. Int. J. Mech. Sci. 120, 159–170 (2017). https://doi.org/10.1016/j.ijmecsci.2016.11.02510.1016/j.ijmecsci.2016.11.025 ↗
83. Li, Y., Xiong, F., Xie, L., Sun, L.: State-space approach for transverse vibration of double-beam systems. Int. J. Mech. Sci. 189, 105974 (2021). https://doi.org/10.1016/j.ijmecsci.2020.10597410.1016/j.ijmecsci.2020.105974 ↗
84. Lim, C.W., Zhang, G., Reddy, J.N.: A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 83, 227–248 (2015). https://doi.org/10.1016/j.jmps.2015.02.00110.1016/j.jmps.2015.02.001 ↗
85. Luo, W.J., Liu, T.Y., Chai, T.J., Yan, J.W., Guo, W.J.: Fast processing of bending deflection for Euler-Bernoulli beam under different boundary constraints based on a semi-analytical null space method. J. Nonlinear Math. Phys. 30(4), 1739–1757 (2023). https://doi.org/10.1007/s44198-023-00155-z10.1007/s44198-023-00155-z ↗
86. Luschi, L., Pieri, F.: An analytical model for the determination of resonance frequencies of perforated beams. J. Micromech. Microeng. 24, 055004 (2014). https://doi.org/10.1088/0960-1317/24/5/05500410.1088/0960-1317/24/5/055004 ↗
87. Maiza, Y., Bourouina, H.: Non-local response prediction for FGP sandwich microbeam with 2D PSH network subjected to adatoms-substrate interactions and exited by magnetic intensity. Acta Mech. 236, 259–288 (2025). https://doi.org/10.1007/s00707-024-04149-w10.1007/s00707-024-04149-w ↗
88. Manolis, G.D., Dineva, P.S., Rangelov, T., Sfyris, D.: Mechanical models and numerical simulations in nanomechanics: A review across the scales. Eng. Anal. Bound. Elem. 128, 149–170 (2021). https://doi.org/10.1016/j.enganabound.2021.04.00410.1016/j.enganabound.2021.04.004 ↗
89. Mektout, M., Bourouina, H.: Nonlocal dynamic response of FGP sandwich microbeam with 2D PSH network incorporating adatoms-surface interactions energy under magnetic field. Mech. Adv. Mater. Struct. (2024). https://doi.org/10.1080/15376494.2024.239498710.1080/15376494.2024.2394987 ↗
90. Merzouki, T., Houari, M.S.A.: Nonlocal strain gradient theory for free vibration analysis of FG nano-scale beams in thermal environments using an efficient numerical model. J. Vib. Eng. Technol. 12, 8775–8800 (2024). https://doi.org/10.1007/s42417-024-01389-x10.1007/s42417-024-01389-x ↗
91. Meski, K., Boutrid, A., Menasria, A., Bouhadra, A., Mamen, B., Tounsi, A., Cuong-Le, T.: Analytical modeling of flexural behavior of advanced composite sandwich beams under nonlinear hygro-thermo-mechanical loads. Multiscale Multidiscip. Model. Exp. des. 7(5), 4701–4719 (2024). https://doi.org/10.1007/s41939-024-00414-610.1007/s41939-024-00414-6 ↗
92. Moreira, R.A., Guzman, H.V., Poma, A.B.: Characterization of structural and energetic differences between conformations of the SARS-CoV-2 spike protein. Materials. 13(23), 5362 (2020). https://doi.org/10.3390/ma132353610.3390/ma1323536 ↗
93. Murmu, T., Adhikari, S.: Nonlocal elasticity-based vibration of initially pre-stressed coupled nanobeam systems. Eur. J. Mech. A/Solids 34, 52–62 (2012). https://doi.org/10.1016/j.euromechsol.2011.11.01010.1016/j.euromechsol.2011.11.010 ↗
94. Narita, F., Wang, Z., Kurita, H., Li, Z., Shi, Y., Jia, Y., Soutis, C.: A review of piezoelectric and magnetostrictive biosensor materials for detection of COVID-19 and other viruses. Adv. Mater. 33, 2005448 (2021). https://doi.org/10.1002/adma.20200544810.1002/adma.202005448 ↗
95. Nguyen, N.-D., Bui, V.-T., Trinh, L.C., Le, Q.-C.: Elastic foundation effect on the small-scale analysis of functionally graded porous microbeams using a modified strain gradient theory. Int. J. Mech. Mater. des. (2024). https://doi.org/10.1007/s10999-024-09735-310.1007/s10999-024-09735-3 ↗
96. Nickabadi, S., Ansari, R., Rouhi, S., Aghdasi, P.: On the derivation of coefficient of Morse potential function for the silicene: A DFT investigation. J. Mol. Model. 27(6), 190 (2021). https://doi.org/10.1007/s00894-021-04780-710.1007/s00894-021-04780-7 ↗
97. Öchsner, A.: Classical Beam Theories of Structural Mechanics. Springer, Cham (2021)10.1007/978-3-030-76035-9 ↗
98. Odira, I., Byiringiro, J., Keraita, J.: Probing multimode thermoelastic damping in MEMS beam mass structure. J. Vib. Eng. Technol. 12(3), 4561–4570 (2024). https://doi.org/10.1007/s42417-023-01137-710.1007/s42417-023-01137-7 ↗
99. Olotu, O.T., Gbadeyan, J.A., Agboola, O.O.: Free vibration analysis of tapered Rayleigh beams resting on variable two-parameter elastic foundation. Forces Mech. 12, 100215 (2023). https://doi.org/10.1016/j.finmec.2023.10021510.1016/j.finmec.2023.100215 ↗
100. Ong, O.Z.S., Ghayesh, M.H., Hussain, S.: Size-dependent dynamics of double-microbeam systems with various boundary conditions via modified couple stress theory. Microsyst. Technol. 27(8), 3193–3210 (2021). https://doi.org/10.1007/s00542-020-05183-z10.1007/s00542-020-05183-z ↗